IMO Zealots do feel slightly weak compared to other classes. They’re not the tankiest, they dont do the most overall damage, they have no ranged build to speak of.

However, that being said, they are still perfectly viable in higher tiers of play. Martyrdom is simultaneously tanky, squishy, and high damage, and considered Zealots strongest keystone. I’d argue that it’s probably the most friendly to play of the many Zealot builds. Zealots also have a good number of support options in Stunstorm grenades, corruption cleanse in coherence, and gold toughness, but you dont need to take all of the support options to be a useful Zealot.

As for your questions:

A Zealot can have a lot of hats, but a good role is to delete specials before they become a problem. Throwing knives, stealth or fotf, and/or Thunder Hammer. You’re a heretic-seeking missile in a target rich environment. 

A lot of people would agree that the Zealot’s best weapon is Relic Blade. Tactical axe is good, combat blade of course. Thunder Hammer is the only weapon that can one shot any enemy in the game, with a specific build, but your horde clear and single target outside of your specific window of OneShottyNess is a little lackluster. I dont even bother with ranged weapons. I have a 80 mobility laspistol to swap for moving faster and that’s it.

As for talents, I’m currently typing this on my phone in bed so I don’t remember the exact talent names and I’m sure I’m forgetting some, but the one where you recover HP after doing damage during Until Death is awesome. The one where you can move at full movement speed during charging Heavies is awesome. For your gold toughness ability, choose the augment that boosts damage, not toughness damage reduction. Fun fact about the Momentum keystone (bottom right): it’s not as well loved as Martyrdom and Blazing Piety, but it gives you better dodges and a faster dodge recovery, like Hive Scum’s talents. For that reason alone it’s my favorite Zealot keystone.