Can you run 2 wires into one breaker?

This is called "double tapping" and by an reputable electrician is looked down upon. A previous comment states that it doesn't diminish the effectiveness of the breaker; it actually can diminish it because the breaker is designed to hold one conductor not multiple.

I would compare that to saying putting two people into one seat belt doesn't diminish the seat belts effectiveness. It wasn't designed to hold two and even though it works it can lead to failures and trip breakers and possibly start fires.

This should never be done, it's against the electrical code, and is a fire hazard. If your going to update, call your power company to see if incoming line and transformer are large enough. Code states each circuit must be on breaker. A 20 amp breaker can carry 15 amp load, 75% of it rating. Some places require a permit. Have a licensed electrician do this for you.

While it is, most certainly, a technical no-no, and you certainly wouldn't want to have it inspected in anticipation of listing it for sale in that condition, for your own use, if you know where both circuits run and what's being run on them and one or both are used minimally, then it's usually not a problem I've done it myself, and seen it done many, many times, just be sure the second circuit on the breaker is for something with a small electrical draw.

That is a practice that has been going on for years. I'll probably be guilty of doing that myself soon. If you're running 14ga wire, you can run two lines into a 15A breaker. 12ga wire you can pair two into a 20A breaker. An electrician probably will not be excited about it, but the effectiveness of the breaker is not diminished.

yea, previous owner doubled up on the load because the undersized panel.

you could always get and install minibreakers but that's kinda looked down upon.

If you can, seperate those loads.