How do I know if a rim is compatible with my car?

I’m getting confused by all the numbers involved. Here’s my current understanding:

• Bolt pattern needs to be an exact match (ex/ 5x114)
• Diameter needs to be exact match, but there’s some flexibility with width (ex/ 17x7 and 17x8 are probably interchangeable)

Things I’m confused about:

• Does offset need to be an exact match? (ex/ ET45 vs ET42?)
• How careful do I need to be with tire size, if the rim is correct? For example, if my car originally had 225/50R17, can I use a 225/65R17 tire?

Is there a good website for explaining these details? I’ve spent time on various wheel database websites, and they only give a list of sizes without explaining why they’re compatible or not.

Thanks!