Hi dexisss
there is simply no other play here with TT than to shove. there is over 1000 in the pot and you'll pick that up alot by shoving which is awesome anyway. not to mention that you should be getting called by hands like 88, 99, AK, AQ all of which you're ahead of and some of which you crush. this isn't a squeeze play, this is a value shove. a squeeze would be if you had 78s and expected them to fold. in answer to your questions:
TT is more than good enough for it
my shoving range would depend on if the button opens to 3x all of the time. if i have seen him use different sizings i'll usually assume bigger sizing=bigger hand till proven otherwise, but on the assumption this is his normal raise size and he was a player who understood opening somewhat wide on the button i'd shove:
22+ KTs+ QJs KJo+ JTs A2s+, A8o+
something like that. TT is the 5th best preflop hand in poker, against a button raise (who should be opening at LEAST 25% of hands, if not anywhere up to 100%) and a small blind call who should never have TT beat...TT is nothing short of a monster that you are looking to get in preflop or take the pot down. nothing good can come from just flat calling.
-F18