I'll try to answer as best I can.
Your count will be those that are uploaded and matched. As you don't have any purchased music in your library then it will basically be the size of the library, so keep that below 25,000 until at least the initial match has finished.
You add songs to your phone for offsite use by selecting them on the phone App and downloading them. You can do that my song (by clicking the cloud icon next to it), or by album, artist or playlist by clicking "download all" at the bottom of the list. Personally, I would create a playlist on iTunes, wait for it to appear on your phone and then download it all.
Deleting them from the phone is more problematic (although I haven't done this yet). Somebody else will probably be able to help with the best ways of doing this, but I'm pretty sure that you can't delete items from the cloud via your phone, so no worries about accidently doing that.
I know that you delete songs by swiping across them and confirming delete. If you swipe across an artist and select delete it will delete the tracks that you have downloaded by that artist. There may be some tricks to make things simpler though.
You can go into Settings/Music, and turn the "show all music" toggle off, which will mean that just those songs on your phone are shown which may help with deciding what needs deleting.
I can't help with the last question I'm afraid. Are there any songs that have problems (i.e. ineligable) in the playlist?