Whatever material that rim is, it's completely unfit for further use. The area around the spoke has completely pulled out from the rest of the rim. The rim's structural integrity is in doubt, plus it is also out of true.
In principle, there shouldn't be any objective issue running one alloy and one carbon rim, provided you changed the brake pads for the new alloy rim. The brake pads for carbon and aluminum rims are made of different materials. You may not see effective braking using a carbon pad on an aluminum rim. Otherwise, it's mainly an aesthetic drawback to have mismatched rims.
For your stated use case, alloy rims will provide better braking, especially in the wet, than carbon. Carbon rim brake rims are expensive and slightly higher-maintenance toys. There is nothing objectively and intrinsically wrong with liking expensive toys, however. Also, I don't believe this failure mode is common on quality aluminum or carbon rims. For carbon rim brake rims, the higher-maintenance bit mainly amounts to using different brake pads, plus you should probably be more conscientious about cleaning the rim surface after wet rides (remove grit, reduce wear), plus your braking in wet rides will be poorer, plus on extended descents (which not all of us do) you need to be conscientious about braking in pulses (don't drag the brakes, this can melt the resin in the rims after too long).
For the cassette, if you consistently changed your chain before it got too worn, the cassette is likely to still be quite usable. If it is worn, then you should recycle it, as it is likely to cause wear to a new chain. Generally, chain checkers are pretty cheap, and I do recommend that most cyclists get one. However, your local bike shop will generally check for you. The issue with cassette wear is that it is hard to assess visually unless the cassette is very obviously worn (and if it's that worn, it's too much too late, and a new chain would skip on the cassette anyway). Basically, if a new chain skips on the cassette, replace the cassette.
In general, it's often possible to acquire a new rim and rebuild the wheel. In addition, some wheel companies may offer a crash/damage discount on parts, even if the wheel is out of its warranty period or if the damage was clearly the user's fault. It doesn't hurt to ask Fulcrum, although they may not do this. (NB: this does look like a warranty case if you're still in warranty, and I'd suggest asking the store that sold you the bike about this if you think you might be in the warranty period.) Outside of replacing with OEM parts, you or your local bike shop could usually lace an aftermarket rims and spokes to the hub if you were not able or willing to source a replacement rim from Fulcrum (which might be relatively costly). However, some Fulcrum wheels use an unusual spoke arrangement where there are two drive-side spokes for every one on the non-drive. If there are 21 spokes on the rear hub, then standard aftermarket rims are not made in this drilling and you would need a Fulcrum replacement. For at least some Fulcrum wheels, there are no spoke holes in the rim bed, and a wheel builder may need to use special tools to insert the nipples. It's possible that your local bike store may be unable to handle this on their own. If either of those are the case, that might push you in favor of trying to source a replacement wheel or set of wheels, especially considering the rim brake market is probably relatively weak.