OOC -
Gorgamesh has no relevant spell and has the Weak Spontaneous Magic flaw (as I've just noticed). This means you can only cast Non-Fatiguing Spontaneous Magic (p. 81), which sucks. For an Intellego Vim effect, your Casting Score is (assuming a -3 aura) 15, which divided by 5 gives a level 3 spell, which is too low to be useful. Using Ceremonial Casting (p. 83), adding Artes Liberales and Philosophiae which for you add +2 to the Casting Score, bringing it to 17, which dividing by 5 and rounding up (I think...) comes out to spell level 4; still very weak. Coming up with a useful level 4 spell is... a challenge. Taking the lowest level guideline, base 1 InVi, allows you to detect magic of tenth magnitude (i.e. spell level 50) or higher. Adding smell magical sense (p. 114) adds +2 magnitudes, and a duration of concentration (p. 112) adds another +1 magnitude; since the spell level is below 5, each magnitude adds just 1 spell level, bringing us to spell level 4, as desired. So, you can sniff out a level 50 or stronger effect, on the wall or door or anywhere else you wish to sniff.
The SG should decide if these are stressful circumstances; if so, you should roll a stress die, just to see if you botch (this is as per the Weak Spontaneous Magic flaw description).
Now Ilshana.
Well, I don't see why you can't try. The most obvious choice is to try to dispel an Hermetic Mentem effect with Perdo Vim (p. 160). The dispell is at Personal range, Momentary duration, and Individual target, so no change is needed to the (General) guideline. Your Casting Score (with a -3 aura) is a rather low +4, so you need to roll a stress die and add +4. Try not to botch

Then, since you're using Fatiguing Spontaneous Magic (p. 81), you divide the total by 2;the result is the spell level you've cast. (You also expand a fatigue level, but you can rest for a few moments after casting the spell, to regain your spirits.) As described in the General guideline, you then need to add 4 magnitudes (each additional magnitude adds +1 spell level until you reach spell level 5, and from then any additional magnitude adds +5 spell levels) plus a stress die (no botch). This is the level of the spell you can dispell; if it's higher, then you failed to dispell it.
For example, say you roll 6 on your spell casting roll. Adding the +4 Casting Score to it, you gain a Casting Total of 10. Dividing by 2, you get a spell level of 5. Adding 4 magnitudes amounts to adding +20 levels, and let's suppose the other stress die came out 5 for a total of level 30. If the Mentem effect that affects you is of level 30 or less, you broke free from it. (SG's decision.)