Please spend a few bucks and take it to a good shop and inspect/repair properly, not just plug at home. It’s worth it.

Plug it’s from the outside, it will be fine

As long it’s not from the side, I use tire repair kit from amazon. Rapid fix, always in the car, doing 90mph no bother, no vibrations on the wheel 👍

Based on what I see, yes.

From what I can tell you have two options to repair it either take it to a good reputable tire shop or by a tire plug kit