(a) It's important for everyone to a degree, but it doesn't mean that a lack of those extra curriculars is insurmountable at any particular stage. It's certainly not insurmountable for you. The typical work experience if you're aiming for the Bar would be mini pupillages and marshalling, as well as other things such as mooting, helping out at a law clinic and so on. However, other experience can also be useful if you can demonstrate that it has some relevance to the skills you need as a barrister. I'd certainly think the placement that you have would fall into that category. Every set has their own mini pupillage policy. Some don't offer it to non law undergraduates, but others do, so find your local chambers and have a read of their policies to see if it's worth applying.
(b) In general my advice is that a Masters doesn't add much. However, frankly most candidates do a Masters to try to elevate poor or average academic profiles, and in that sense they're not as useful as candidates want them to be. However, they can be of more use in your case, that is to say candidates with very good academic profiles who want to take things once step further and really elevate that part of their application. Usually that is because the post graduate courses are done for intellectual reasons and not to tick boxes. That sort of thing is most useful for commercial and similar pupillages, particularly at higher end sets. Those pupillages are extremely competitive by definition, but if you look at profiles of recent tenants you will see a range of additional academic achievements beyond the usual, and particularly with well known or more competitive courses. So actually, from what you've said about your own situation, I expect a Masters probably would benefit you. Even if you didn't want to go for one of the top end pupillages, you've got the potentially to build a very strong application with the route you're looking to take, and it really does help that it's done out of genuine interest too. Makes you a more genuine and attractive candidate because you've pursued, and have expertise in, areas that you are actually interested in.