1. Parallel compression (as I understand it) is the idea blending two versions of the same audio source: one compressed, one uncompressed, or one compressed heavily, the other compressed lightly, etc. The most common example I've seen is setting up a send bus where the signal from a completely dry drum mix is also being sent to an auxiliary or return track that has a compressor processing it, then blending the two signals on your mixer to achieve a balance between a full, loud signal and a preservation of dynamics.

2. Because you think the sound needs it! Compression of any sort is like any other type of post-processing: It's not something that is applied as a general rule, but as an effect to enhance or repair a sound based on what it needs.

I use parallel compression to usually fatten a sound. I have an aux send of the same signal thats heavily compressed then slowly mix it in

Basically a duplicate audio source mixed in together: one with compression, the other without.

There's a fair few advantages to this. Say for example your material has a lot of quick peaks and transient hits - like a percussion loop - and you want to bring the floor up and beef up the percussion itself, but without the compressor bringing the peaks down. Attack timings can only get you so far in this case. Instead, duplicate the loop, compress one copy quite heavily to bring the body out, and then mix it together with the old copy that still has the peaks. You end up getting the best of both worlds this way.

On a lot of newer software compressors, they now include a 'Dry Mix' knob that helps do this for you. It's great for making dynamic material more 'beefy' without compromising it's attack too much.

In some tutorials and guides, they often refer to this as 'New York Compression', if that also helps!