What happens with iTunes Match after my library exceeds 25,000 songs?
The 25,000 songs is for the songs that you've added to itunes match and are not purchased from the itunes store. If you exceed that limit you will just be able to able to add to your itunes match library, songs that are purchased from itunes. 

You can delete specific songs from your icloud library (right click>delete from icloud), there is no need to delete them from your local library too.

And yes, it just displays a popup mentioning that you've reached the  limit.

This is all documented at https://support.apple.com/en-us/HT204146