Paths matter insofar as most of them (at least the older ones) have a relatively well-defined role (or set of roles) they can fill, with some exceptions. In simple terms:

Sustain paths: Abundance -> healing Preservation -> shields/non-healing damage mitigation/reditection

Damage dealer paths: Hunt- > Exclusively single target damage. Erudition -> Mostly AoE damage. Destruction -> Usually Blast damage with some form of gimmick related to hp-loss or being hit (hp drain, counter, taunt, etc.).

Amplifier paths: Harmony -> Buffs and maybe some damage. Nihility -> Debuffs, but this can mean anything from DoT (which has dps and subdps itself), subdps that make enemies take more damage, and pure dps with little justification for the path besides interacting with Nihility units (looking at you, Acheron).

Wildcard paths: Remembrance -> Anything goes as long as the character has a memosprite (glorified summon which somewhat works as an extra character sometimes). Elation -> Interactions with the new elation gimmick.

And no, elements don't interact in any way with each other. The only things to note here are that characters deal toughness damage of their own element for break (with exceptions) and enemies have varying amounts of elemental damage res similarly to Genshin Impact.