Does turning on and off modem hurt and ISP question?

It varies with your provider.

No, there normally shouldn't be a problem if you want to power off your modem every night. Some providers are more likely to dump your IP address (if it's a dynamic address). Some provide static addresses that never change. And some provide dynamic addresses but they last weeks or months before they change. They do eventually recycle the addresses to other people.

Some people prefer dynamic addresses. They're usually considered more secure, and they prevent someone from repeatedly targeting your individual computer for a break-in, etc. Others prefer static addresses if they're regularly gaming, or connecting to their computer from work, etc.

And for what it's worth, ISP means "Internet Service Provider." That's who you get your internet service from. And there's no such thing as an ISP address. It's "IP Address." IP is short for Internet Protocol.