Welcome to FT
flyin ' ruddl 
1) Officially you will not get into SQ lounge without onward C or F ticket on SQ, LH or NZ (only), unless as PPS. Unofficially, if you wait until 1:30am (just a guess - after the last flights are boarded) when all is quiet you may have a chance of sneaking in
2) You can walk along the passageway (by the E gates) between the terminal - complete with moving walkways if desired.
3) Not sure - try a transit hotel (will cost $$).