Acoustic Strings on a Classical Guitar

A good three years ago, when I was first starting guitar, I never realized that my "acoustic" guitar was actually a classical one (I ignored the warning signs; nylon strings, etc.)

Knowing that, I bought acoustic steel strings and put it on, and it's been that way for a long time. Within the past month, I've taken it out of the cellar and started to play it again, and I have really gained back my love for guitar, albeit it is extremely hard to play (the action is pretty high and it hurts to play)

Thinking it was the fault of my saddle, I sanded it down a little to make it a bit more playable (it made no difference)

I just bought nylon strings that works for a classical guitar, and although the neck is a little bit warped when the strings are on, taking it off leaves only a teensy curve in the neck.

During this time, I got used to play with a pick and playing country songs, and I'm wondering if 1. My guitar is just cooked due to the acoustic strings, and 2. Am I still able to use a pick and play strumming songs like if it was an acoustic?

Thanks