I wanna find out if this is against the TOS or not. I would like to place a "welcome page" that basically tells the user to download firefox to access the site (I will put my referral block there), if the user has any other browser, he/she will not able to see it. It will be a firefox browser only site
I would assume that is against the TOS. That's like encouraging users to click on ads. Instead of telling them to download Firefox, you could say it's required to view this site and set a link; that may be a bit more valid.
Im not too familiar with the adSense ruels, but how would it be a problem if there wasn't any adsense on the page in question?
A better way might be instead of telling him to download firefox to access the page, you could put it "This site is best viewed using FireFox in 1024X768 Resolution" or something along those lines. I would personally e-mail google and see what they think before making any changes you are unsure of.