Forget - and I mean it - about checking luggage through. Won't happen. Technically, SIN does have ways to retrieve your baggage from the baggage claim (after immigration) and re-check it for you, but that process is rather unpleasant. As long as your nationality (Which you REALLY should state if you ask such questions..!!!) allows entry into Singapore, just go landside and check at Jetstar counters.

If you travel with hand luggage, then you can stay airside indeed. Please note that airside isn't "clean", there is security at every gate. So, no drinks/water etc.

All terminals in Singapore are connected to each other (airside, as well as landside), so for technical reasons, it's more like a single huge terminal.. you can walk or ride the trains to shortcut it.. SIN is a fairly big airport but it's not gigantic.

Oh, and don't try to gamble on bringing overweight luggage onto a LCC carrier. Sure, you might get lucky. But if they catch you at the gate, being quite a bit over the limit, you won't be happy with the "options" offered.. you're getting your baggage "tagged" at checkin.. if you show up with "untagged" baggage at the gate, VERY good chance you're picked for some "special" check.

SilkAir is the LCC from SQ. You're only getting benefits when you're a SQ Elite member. No *G benefits, including luggage. They're "only" half-LCC, ie for the same price, I'd probably prefer them to Air Asia, JetStar.. but they're NOT a full service carrier. Somewhere in the middle.. for a one-way SIN-SGN, without holding SQ Status, and as long as luggage fees don't play a role, I'd hardly pay more than maybe 20SGD extra for them over a LCC (direct flight, schedule similar)