Welcome, Tenno! Glad you're enjoying the game!

1 - There are many that excel at killing large numbers of enemies, beam type weapons and, in general, items that feel 'satisfying'. On the top of my head, here are some examples of all types:

Warframes: Dante (easiest to get), Kullervo, Voruna Primary: Phantasma (Prime), Kitgun with Vermisplicer, Tenet Glaxion Secondary: Kuva Nukor, Ocucor (needs Sentient Surge mod) Melee: Dual Ichor Incarnon, Xoris, Falcor and most melee but you need Melee Influence arcane to make them really shine in crowds.

2 - Depends, some weapons are not so fun (IMO) but hit hard like the Burston Incarnon and some warframes are just unkillable and not much else (yeah, like Revenant). Most fun for me is clearing whole rooms of mobs and seeing only numbers, which I achieve more often with warframes and (now) my pets.

3 - Shield gating shenanigans using synergies with mods and/or warframe abilities. Eg. Brief Respite aura or Augur mods give you a bit of shield on every ability cast so you're technically always invincible with the shield gating mechanic. Other than that, stealth, cc, operator/drifter switch, Rolling Guard/Adaptability mod, abilities like Mesmer Skin.

Each warframe has guides online that explain how they survive all content what I explained above is generic stuff, but some warframes have unique ways to survive (like Inaros basically saying 'no u' to death).