You can use a hacksaw, but you'll get a cleaner nub with a pipe cutter. You want it to be squared off and no burrs which is possible without a pipe cutter, but more work.
If you put a little oil on the threads, it seems to snug up easier, but isn't required. You shouldn't need much after finger tight. The valve should not easily be able to be rotated on the pipe, nor should it pull off. Use two wrenches, one on the nut and the other on the valve body.
Seems most of the hoses for toilets are 3/8". On a 1.6g flush, that's plenty to get it to fill quickly; go with what you can find. It has nothing to do with the quality of the flush, so who really cares.