Cutting melamine can be done with a coarse blade on a circular saw if you don't care how it looks when you're done, it all comes down to final appearance. They make super-expensive blades specifically for cutting melamine cleanly, you can use a dual cut table saw... there's just tons of "go get a bank loan" options. For the rest of us who don't have professional cabinet makers and friends, there are other options. I've seen people get perfectly decent results with tape on the underside cutting with a circular saw and finishing blade. There's a lot to be found online if you do a search for "cutting melamine".
Personally, when I built my cage, I just had Home Depot cut the pieces and called it good. It wasn't perfect, but it was pretty damn close and (more importantly for my needs) the sizes matched each other. If you're trying to match cuts to existing things you may need more fine tuning than I did. One of the dimensions I had them cut came out an inch longer than I asked, but they were all the same amount over in that dimension so it still fit perfectly.
For drilling I just used a basic hand drill with ordinary wood drill bits. They'll cut a hole cleaner than the head of the screws you're using, no problem. If you want to relieve your pilot holes for the heads so that the screws are more flush-fit without crushing the melamine, find a drill bit that's about the same size or just a bit smaller than the head of the screw and then hand turn it to shave a funnel into your pilot hole. If you use a drill (like I did for the first few) you'll almost always send it too deep. It's a good hand workout to hand-relieve those pilot holes, but except for the odd shattered wine glass I've never regretted having better than average grip strength.
As far as the tub size and Flexwatt questions go, I'll defer to people with more expertise on the matter than I have.
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