I'm flying SQ Business SIN-NRT and connecting to ANA in NRT using separate tickets. We'll have nearly 3 hours just in case they don't, but will SQ check my bags all the way through to the final destination? Certainly being Star carriers they've got an interline agreement correct?
SQ can and most probably will check your bags through in this case.
Note that having an partnership doesn’t mean an airline is obligated to check your bags through on separate tickets.