1) Are there any other recommended ways to try to determine which genes in a bacteria are "differentially expressed" in response to a treatment (here UV radiation)? Is RNA-sequencing the preferred way to do this? I am only asking because you stated that "most reads will map to the highly abundant rRNA", and I was uncertain if that was a good or bad fact (or just a fact to not worry about).

I think the best approach would be total RNA sequencing. Your genomics core lab might have a way to enrich bacterial mRNA and deplete rRNA. If they can't then understand that a large proporiton of reads will be rRNA. This means there will be fewer reads representing other genes. The total number of reads required for the experiment will need to be higher if rRNA is not depleted first.

2) Would the procedure for RNA-sequencing for bacteria be similar to that for eukaryotes? I am assuming I would still want "replication"? I guess I am used to one "replicate" being one specimen for eukaryotes, but in the case of bacteria, one "replicate" would be one culture (a Petri dish perhaps) of bacteria specimens?

In eukaryotes, it is common to deplete rRNA using either specific degradation (Ribominus/RiboZero) or mRNA enrichment using oligo dT beads. Bacteria don't polyadenylate mRNA so that won't work. rRNA depletion kits are mostly designed for mammalian analysis, you'll need to see if there's one for bacteria. If none exist, then you're options are limited to total RNA seq with the caveat that most reads will map to rRNA.

3) In prokaryotes, is it still possible to do downstream analyses? Such as GO and pathway analyses of the DEGs?

Yes, although you'll need a database that maps bacterial gene names to GO annotations.

4) If you happened to have analyzed both eukaryotes and prokaryotes by RNA-sequencing, are there any differences or warnings you would recommend to somebody new to prokaryotes?

The major consideration is the quality of the reference genome and annotation databases. Bacteria can be very diverse and not all of them have high quality genome assemblies or annotations. If these resources are high quality (like human and most model organisms) then it makes the downstream analysis much easier. If you have good quality reference data, then bacterial analysis could be more simple in that you don't need as many sequence reads to get good transcriptome coverage due to fewer genes.