Is it alright to pour heated tomato sauce back into the jar along with the fresh new sauce?

Sure you can, but just remember that you will have added more bacteria to the jarred sauce than was there before *IF* the jarred sauce had always been covered and relatively recently-opened, and the heated sauce was older and/or exposed to more air. Otherwise, the heated sauce will have potentially fewer bacteria** from the heating than the jarred portion.

Keep in mind that tomato sauces, etc, are a little different because acids (like tomatoes) are natural preservatives and will keep more bacteria from growing in the same amount of time they'd grow in other foods that don't act as natural preservatives. (They may also contain salt, another natural preservative.)

** there are always bacteria, it's a matter of how many have had time to grow and the type

It's o.k., just remember you heated it once already, so the next time you might as well go heavy on the sauce, and not reheat it again. Only once.

With anything like that I keep leftovers separate. I'd probably use that up in a soup.

I would. It's not a meat or dairy product, just tomatoes, liquid and seasonings.

It`d be fine. I`ve done it lots of times with never a problem.

The bigger question is why did you heat it in the first place?

No, always keep them separate.

yes.

#yolo