It says that modifying Save files to your advantage is banned. Does it also apply to saving to heal mid-run?

No. Saving is allowed.

Good. I saved three times though out the run, and I was worried for 2 things.
1. That I may lose my run to low health
2. That the run may be rejected when I submit it.

saving is an ingame feature, theres quite literally no reason for it to count as save editting. save editting is specifically when saves are editted directly in the save files.

By modifying saves, it means that you can't modify your save files, not that you can't save.

thank god because i was confused when i submitted my first run on the Jevil% category i saved so i could
1. Heal
2. If I die on jevil i could easily respawn and beat him

Yes, you are allowed to save, By Modify they mean edit the save file so that you can go through it faster or something.