Is it 'safe' to use a 700 x 47c tyre on a rim with inner width of 15mm?
To fit 700c (ISO 622) wheels into a bike built for 27" (ISO 630) you only need to shift the rim brake pads down 4mm. If you're exceptionally lucky your current brakes will have enough reach and you'll just have to adjust the pads. That's the first thing to check, because if that doesn't work there's no way you're going to do this on a $50 budget.

2" wide tyres should be ok on the 700c rims. Not ideal, and probably outside the manufacturers specifications, but it should work. I've done that with 406 wheels before and it's worked pretty well.

The real problem is the tubes. Again, new tubes overstretched like that would work in a pinch, but they're be extra vulnerable to punctures because of the stretch. But usually if you're replacing aged tyres I'd suggest new tubes since they're likely to be in similar condition. Trying to over-stretch old tubes is very likely to fail immediately, and if not will almost certainly fail shortly after you start riding.

If you can get the 700c wheels to work, I'd go with a 38mm tyre rather than 42 or 48, just because I'm really wary of damaging the tubes. I assume on your budget you can't afford to carry a spare. But really, if you're doing a ride of any length I think you should buy at least one spare, unless it's a ride you can bail out of and get someone to carry you and your bike home. Even a cheap, shitty spare tube is better than nothing. personally I would cheap out on the tyres in order to buy a couple of tubes. It's not worth going out on a ride and having to go home because your old tubes give out.

If you can't make the brakes work I suggest buying the fattest 27" tyres that will fit your tubes, which is likely to be 1 3/8". I'm sure I've seen 1 1/2" x 27" tyres but I can't find any now.