MacOS – iTunes asks me to subscribe to iTunes Match again when I try to turn iTunes Match back on

You may not be able to get complete matches, but here's what I have been doing in the cases where one or two tracks don't match.

1. Select the item(s) to attempt to re-match.
2. Right-click on them, and select "Create AAC Version"
3. When this is complete, hit alt-backspace, and choose to remove both the original and the iCloud version. Also choose to delete the items from disk.
4. Go to the "Store" -> "Update iTunes Match" menu item.

Note that this will keep the play counts, etc on your tracks. It may not succeed on every track, and sometimes repeating the process picks up another track.

Occasionally, I'll get a "Removed" icon there after doing this: just right-click and choose "Add to iCloud" on these.

Once it is all uploaded to my iCloud and I delete it from my hard drive, will iTunes still work or will it be constantly be looking for the physical files.

After uploading all your files to iTunes Match you can delete all your local files. iTunes Match needs not the original files.

If I can delete it, how do I upload new music I acquire, do I have to physically put it on iTunes, then upload and then delete?

You answered your question by yourself. That is the correct workflow.

How does it work with my iPhone as I will never have the capacity to load all my songs on the phone. Is it easy to select an album or genre at a time to download to the phone?

A selection by genre is not possible. But you can select by album, artist, playlists, ... .