There's not really much point to taking GSF Illusion despite there being a lot of interesting and useful illusion spells (I know some beg to differ but PhK is lackluster at best)
I suggest taking SF/GSF Illusion should extend the duration of invisibility by the same degree that SF/GSF Divination extends the duration of See Invisibility.
Yes, though definitely NOT improved invisibility. Regular invis only
Oh yes without question. Though if it's possible extension of the invisibility aspect of improved invisibility without the 50% miss chance would be neat for sorcerers.