1. Integers would make the situation easier, but still overflow after ~50 days. You can't just increment delta every frame; frame times vary significantly and and if you aren't precise to the millisecond things will jump around.

2. It's not exactly cheap, and I don't think compilers put much effort into making sure you actually retain that precision. I have only really used floats in shaders though, and don't know what would happen.

3. I'm pretty sure that in practice you'd lose out on a lot of hardware-accelerated functions, doing trig and interpolations with multiple messy conversions. It's also possible you'd fuck up some compiler optimizations.