No. Learn Bash. The biggest benefit of bash is that you're virtually guaranteed to find it on any linux server. It's ubiquity is its strength. Write a bash script once and take comfort in the fact that it will be able to run on virtually any server for years to come. Does bash have a bunch of cryptic syntax and weird quirks? Sure, but that cryptic syntax and those weird works should remain pretty stable in the coming decades.

Depends a bit why you're learning shell programming.

If you want to write scripts for your personal use, or maybe for some project you have then I recommend zsh as it's so much more useful and easier. The zsh User Guide is quite good by the way (not updated in a long time, but still relevant).

I you want to write shell scripts at $DAYJOB or some such bash is probably the wiser choice, as it's just more common. Whether that's a good or bad thing is kinda besides the point here; it just is.

Nope, learn bash. Its the default on every system.

For your interactive shells, of course. There are many conveniences over bash and far better autocompletion.

For scripts? Use Posix sh.