you did not tell us, whether you fly on separate tickets or on one. If on one SQ should issue boarding pass for TG flight in Singapore already; if on two, you will certainly not have to pay airport tax in BKK when leaving airside (but even on one, you might not have to)
Transit desks are now AFTER transit security on departure level. So either you leave airside through normal arrival (and get your boarding pass later at normal check in) or you go through transit security, get your boarding pass and then stay airside (but even from there you can go back landside)
check through luggage is actually decided by SQ in Singapore. for 12-24 hours transit, TG is sometimes reluctant, but so far I always could check through (you have to tell them that you stay airside). But as I said, in this case SQ will decide...