I’m fairly new to DIY home improvement. Are these arrowed parts structural support? I’m looking to vault the ceiling below but I’m not sure if I need to involve an engineer.
You absolutely need to engage an engineer.
Ignoring those braces, which may or may not be relevant, your ceiling joists tie the outer walls together and keep them from bowing outward.
As an aside, this is a challenging project for anyone. It involves (at a minimum) demolition, carpentry, electrical, drywall, paint, plus a healthy dose of code compliance. I don’t know if you were being modest when you said you were new to DIY, but you might want to start with smaller projects in those areas.
That looks like an old house, with the original roof sheathing made out of boards instead of plywood or OSB. The rafters, however, look like 2x6 or 2x8s and not the usual 5x5 rough sawn lumber with pieces of bark you see in really old houses. So an old house, but not too old. Regardless, the issue with old houses is that they were mostly underbuilt, and this is why you see so many old houses with bowing roofs, leaning walls, sagging floors, etc. They don't make houses like they used to, and that's a good thing.
All of this means that those pieces of wood could have been installed there to make up for insufficient rafters when they built the house (ie rafters spanning a longer distance that recommended), or they could have installed them when they put the plywood sheathing over the boards, to straighten those rafters before the roofing job. Or, like someone suggested in the comments, they could be there because the carpenter building the roof structure did not have a helper that day and just used those pieces of wood to hold the rafter in place while nailing the structure together, and then never removed them. Whatever the reason, given that this is an old house with an underbuilt roof, you should not assume that you can just remove these pieces of wood without doing some serious structural make-up work.
But for the sake of the argument, let's say you are dead set on raising the ceiling. You could do that by demolishing the roof and building a proper roof. Or you could sister all of the current rafters to add structural support (contrary to what suggested in another answer, there are no trusses in involved here.) Either way, this is an expensive and difficult job, requiring permits, plans, inspections, and a lot more skills than the typical DIY project. You will also face problems with insulating and venting the roof if you are not planning on a "hot roof" thing, etc., all considerations which depend on your region. Not to mention the drywall, electrical, plumbing (any vents going through), etc. aspects.