New 2024 Tucson Limited PHEV

Hello! I’m a new Tucson owner - just bought my first Hyundai on Saturday. I bought it used - it’s a 2024 Tucson Limited PHEV. Since I bought it preowned from CarMax, I didn’t get the whole learning presentation you probably get at the dealership. I’ve learned quite a bit by googling all kinds of info to answer my questions and actually reading through the owners manual. But I have a few questions I thought I’d ask here if anyone is willing to answer (without being a jerk - seems there are a lot of those 😆)

The car came with a 12 Amp Level 1 Charging cable which I wanted to keep in my garage while I wait to decide if I need to have a Level 2 installed at home… but do I need to get a Level 2 charging cable to keep in the car for public charging stations? Or will they have a cable already for me to use?

And does the car always use the battery first and then transition to gas or will it always use battery under a certain MPH and then switch to gas if you exceed that? I know there are multiple drive modes so I’m still researching these things but would love to learn quickly if any of you are kind enough to help!