In what cases can I use the copyright content on my videos without risk to the channel?

As far as I remember, before, if YouTube found copyrighted content in my videos (or music), it would notify me about it in a notice, and would include ads for the benefit of the copyright holder in those videos. No penalties were imposed on the channel by YouTube. There were no other penalties or restrictions for the channel.

What's the situation now?

Or where is the limit in using copyright content in my videos, so it's not crossed?

What you are referring to is copyright claim for the content used on your video. It won't harm your channel if your channel is NOT monetized. You can use copyright claimed content as much as you want provided that your channel is not monetize. Also, make sure the original owner is not going to issue a strike manually.