There are tons of opportunities to solve convos without a Cha skill.
The convo with Kagha has so many different options other than persuasion to save the kid. Some I've encountered:
Wood elf - Brings up Sylvanus as someone who is intimately familiar with their god.
Paladin - Calls into question her judicial authority and offers to arbitrate instead.
Druid - Brings up some hippie gweneth paltrow scented candles or something.
Hidden religion roll - I think this one only showed up because it rolled in the background (the little 20 in the corner) before the speech options came up. As a wizard, you would probably do well on that roll and have the ability to convince her to stop being a meanie.
Honestly, Insight is by far the most important skill for convos. 90% of your convos with your companions have at least one insight check, and the Cha checks are usually pretty low.
Besides all that, failing rolls is part of DnD. Nothing is a game over (other than your last death save), so enjoy the ride and let the story take you where it will. I will definitely be playing a low Cha Durge at some point and a low Int Pally. Seeing what happens when they fuck up is going to be half the fun.
Maybe but the charisma skills are by far the most common and reliable checks. A lot have other checks as well but those can be all over the place. The most common non-charisma is probably wisdom but that's mostly because of the tadpole and I don't know if it's a good idea to use that too much.