EVOH is ethylene-vinyl alcohol copolymer, which is used as an oxygen barrier coating on PEX tubing amongst numerous other uses.
No, I don't believe it's possible to weld truly dissimilar polymers together. Depending on the polymers you may get an adhesive joint, but that's not quite the same as true weld as far as I understand it.
No, it's not possible to truly weld cross-linked polyethylene material to any other material or to itself, post-crosslinking, for fairly obvious reasons. You need a mechanical joint to connect the two.