You can wear a body protector for any activity, it's not against the rules of any discipline. I have a Racesafe BP which is very comfortable and well fitted, also an air jacket could be an option. It's just like wearing a gilet. As for hats I love my Gatehouse HS1 and my CO Ayr8, both fit my massive head well and are very comfortable.
Any hat has to be mark as PAS 015, as of January 2018 the others won’t be allowed in competition, you can still wear them at home. I have 2 Charles Owen Fiona’s that have been worn about 10 times between them and now I can’t wear in the ring
Another vote for Racesafe, so comfortable the only time I’ve not worn it is when pregnant (doesn’t fit) or when it’s super hot (rare in england!). They have such a good range of sizes that can be adapted I don’t think I’ve found anyone that hasn’t managed to get a good fit. Although if you’re not eventing you could look at an air jacket?
Hats are trickier as you need to go with what fits, the HS1 doesn’t suit my head I’ve got a ‘Champion’ shape head. Get one fitted at a decent tack shop.
You will need an up to date legal hat for dressage, they vary from reasonable £ to £lots! I used to have an air jacket - very good protection. You can wear body protectors for all disciplines - not sure about showing!
I have just replaced my body protector and have an air jacket . Had one before which totally saved my bacon out hacking when my horse slipped on the road and landed on me . Most of the time I forget I’ve got it on - till I get off and forget to unclip it!
I have a Charles Owen pro 2 and I love it, really comfy to wear. Body protector wise I have a really old child's size airowear (I'm tiny!), i only wear it for xc and I haven't done that for ages so it goes a bit solid, really need to get a new one!