NO to both tooth paste and seltzer. Toothpastes have lot of chemicals that will be absorbed by your gums, also seltzer has carbonated water not good for your stomach even when you are not fasting.
To clean your mouth use Sea Salt , brush with it and use tongue scraper to remove the white gunk.
If you know what Neti is you also clean your nostrils that way with Sea Salt water. Lot of smells come thru' your nose. I know because i am on my 19th day and almost healed with most the things.