General comments about structure:
1) I would allow Spell Compendium as well. I think in general everyone ever who has ever seen the book allows it, and it's pretty fucking great.
2) You might want to specify that you are allowing MMI as well, since you are using Alter Self and Polymorph. Just technically true.
3) SGT is actually supposed to be run on "what you would know" grounds, so Wizards prepare spells based on likely enemies in the area. In practice, this is almost never important, because the things you are really worried about fighting (Dragons and Outsiders) can hit you in the desert/cave/ect. But for what it's worth, that's how it is. Doesn't mean they know they have to deal with a Basilisk by any means, but they can prepare in general, although, especially level 5, that hardly matters because Alter Self is going to be probably the best at any level, so you are only changing your level 1 spell.
4) SGT is supposed to be novarific. This does slightly bias in favor of some types of character over others, but as a general rule, you should be casting as many spells as your factotum can each fight. So Basilisk, start with grease instead of tanglefoot bag, and then follow up with Tanglefoot if you have to. As a general rule.
Specific fight comments SGT 5:
0) Traps, I don't know how you plan to identify all the DC 24 traps and disable them all with basically no problems when you haven't put a single rank in search, and you have a +13 Disable Device. So... I guess you can try to use Fighter style trap disarming of throwing things in front of you + ten foot pole, but that probably won't help against the First Alarm Triggered Orb of Acid Trap, or the second, or the third.
1) Basilisk: a) It's pretty clear that you get 50% for using the mirror, because you are "averting your eyes" which only ever gets a 50% reduction. As opposed to total eye closure which gets you 100%. You lose at life everyone who needs to see. b) Also, there is the passive and active gaze, so you have to roll those basically twice per round. Also, you have to give it the miss chance for concealment, even when using a mirror. c) The point of "in it's burrow" is that it wait around a corner, so you can't use range attacks, and if you ever close, you get gazed. Then it stays in the burrow if you pop a shot off and then run away. It doesn't allow kite tactics, which is why this is one of the SGTs that Wizards lose and Barbarians win.
2) Manticore: a) how are you charging into a tanglefoot throw, that's pretty silly, and possibly illegal. b) One thing to keep in mind is that creatures with clumsy fly speeds faster than their land speed can go really far in a straight line by flying at ground level and landing at the end of their turn. Allows them to turn on a dime if they choose, while maintaining speed. Probably makes Opportunistic Piety harder (once tanglefoot wears off).
3) Phase Spiders can see into the material plane from the ethereal, I have no idea how you intend to find it before it finds you. It basically comes down to a readied action each round. I'd need to see this played out.
4) Howler may prove a problem, that would be like Manticore or Phase Spider, where I'd want to roll a bunch of times or do some really complex math to see how that one really turns out, so maybe Factotum always loses to the Howler, and you did the math, but you actually do have decent offense against the Allip, Opportunistic Piety's healing energy can also be used to damage undead, so you can just kill it dead in two rounds (OP never says anything about Will save for half harmless, like most healing effects, and doesn't give any kind of range/attack roll at all. You can arguably just channel and kill some undead you don't even have line of sight or effect to, though there might be something in the Magic Overview section that prevents that, certainly nothing stops you from OPing from 120ft away, moving back 30ft, and doing it again, though I think the Dark Temple would probably involve the Allip coming out of the ground within 60ft of you anyway, giving it a surprise round Babble.)
5) Cleric + Zombies. Actually, that's not EL 7 anymore than it's EL 22 when a Balor uses it's summon to summon another Balor, or a Formian Mynarch has some dominated beatstick. CR/EL is very clear that when something gains minions through the use of it's abilities, it doesn't increase EL at all. So when an NPC Cleric uses it's spells and Wealth to cast Desecrate, then Animate some Undead, that's totally not an EL increase, just like when the PC Cleric animates some undead, they don't add to party level. It's one of the reasons Clerics are Better Than You, (for specific values of you).
SGT 10:
First build. Other than Polymorph, I think you can do better with spells. Especially because:
a) Empowered Fireball is a level 5 spell, how do you even have that, and why do you want it? Can the Factotum apply metamagic without increasing the spell level? If so, why don't you have empowered Twinned everything instead?
b) Empowered Scorching Ray is also a "why do you even want it" thing, but also a "again, can you even have this when you already have a 4th level spell?" It seems really clear to me that metamagic is not free (I can quote you if you don't believe me) and based on the way it's worded, you also can't have two 4th level spells where one is a 4th, and the other is a 2nd modified to 4th. So you have two illegal spells.
0) Again with traps. All the Symbols have DC 30+ search and disable DCs. You have a search of Int.... Search, and you have a Disable of +20, or, not 50%. So for disabling, you get to say "After the first Symbol, my character figures out what they are" (since you probably don't have read magic, and you can't make the search check, although, I think that's bullshit and you should be able to make a DC 25+level Spellcraft check to identify the spell, and even a DC 15+level check to know that the spell exists, and what it does, and operate from there, but RAW symbols are stupid).
That leaves the disabling method of... throwing a covering onto each symbol, then waiting CLX10 minutes (or arguing that you blocked line of effect), and moving on to the next one. So you have to have a lot of coverings, and absent line of effect ruling, a lot of time. You really aren't doing this any better than a fighter, because your skill bonuses are just not high enough.
1) Fire Giant. Not sure about all the stealth hiding stuff, unsure how you get concealment, and it does have a +14 spot to you +15 Hide, so it could totally end up seeing you no problem. But even if you do get into hiding and do your little Grey Render charge (PS Arcane Dilettante heavily implies you still need verbal components if they exist, which polymorph does, but I'll give you this one as RAW) you still need to rethink your strategy, possibly including some kind of grapple buff spells, because you actually a) can't succeed on your grapple initiation that often, b) Would totally lose if you did.
Are you playing with some completely different grapple rules? Because the Fire Giant has a +25 grapple mod, and you in Grey Render form have a +22 mod. You lose a lot, and his winning strategy is to just initiate the grapple himself, and then pin you, then do damage, and you will never succeed on checks enough to win. This is the same winning strategy he would use on a regular Grey Render too, so he doesn't even need to know it's a Polymorph to employ it. Instead, I think you might be better off going for something that avoids ever grappling him in the first place, because if you start with a Bite into grapple, he will voluntarily fail the initial grapple check, then Pin and win. No reason to bother breaking the grapple.
2) Well let's see, both your Empowered Fireball and Empowered Scorching Ray are illegal if you also want to polymorph. Also, there is an argument to be had about if Will-o Wisps are gaseous, as the prevention, but for simplicity sake, I'll buy it. Of course, you still start off with way less damage done, and oh yeah, you totally can't use the Dragon for soft cover against himself. He can originate the breath from any corner of his own space. So take 4 from your ref save, and remember that you only get haste for 10 rounds, and he's going to be spending a lot of time taking long sweeping breath runs at you to avoid letting you shock him, so that will probably only handle the first couple breaths.
3-6) Genuinely confused why you think it will beat Trolls, Shadows, Mind Flayers, Vrock. Vrock maybe, and Shadows, depends a lot on how damaging the surprise round and subsequent rounds are, vs how many you can turn at a time. And I don't want to do the math, especially if there's a better strategy I haven't thought of yet. But I'm starting to think you are assuming the Factotum can just surprise round everything and never be surprised himself, which doesn't seem to have any mechanical basis on your current build.