Installing a chainguard on a bike with derauiller
This StackExchange site has its limitations, in that product recommendations are not allowed because of regional differences and products/pricing going obsolete. However I think the answers are no you don't have to break the chain, remove the derailleur or lock off any gears. Products exist but are quite unusual so you will have to do some searching online or in bike shops in your local region.

Using Google, I found a couple of examples. The first one I got to a website which sells chainguards and browsed through the ones which say compatible with a single gear, and discovered some which say compatible with a triple ring like this style:



Another Google search along the lines of "chainguard triple derailleur" and I found this image, which has a more conspicuous allowance for the derailleur to remain fitted and usable: