I was accepted for vectors at IS around August I think, and the turnaround was within about 2 days as I recall. The photo acceptance turnaround was pretty quick too back when I did that. Things may be a little backed up because of the new applications being closed for a few weeks and because of the holidays though. God luck.
As far as the rest, on SS you need to go through the normal process. Turnaround on apps pretty quick. Note that here you can submit bitmaps if you want just to get in the door. The reviewers there can be a bit quirky with vectors. At SS, you can submit vector versions and bitmap versions of the same file. Refer to the forums there for particulars, or PM me.
DT - There is no real "application" - you just submit ad they ake what they want. You will need to submit a bitmap if the file, then attach a vector "additional format". The bitmap will be approved first, usually within their normal time frame of 5 or more days, but then it can be up to 21 days (and even more) for the vector format to be approved. Yes, stupid I know. This stupid process is surely a revenue loser for them. As a buyer, I would not wait 3 weeks for a vector file to appear.
Stockxpert - just submit the number required on the application - I think it is 5 images but not absolutely sure. It's been awhile. In any event, there is no separate app for illustrators, so you could send fractals, photos, anything. I think my orignal app here got stuck in some weird limbo and it took awhile.
123RF - I think 10 files are needed for an application. Been awhile so can't remember exactly here. No separate application for vectors, just submit your best work.
Bigstock - just submit - there's no "formal" application - they'll just take what they feel will sell.