It probably won't hurt you, but I wouldn't risk it, just in case. Glazes for food containers are unlikely to contain lead, but may have other metals that are harmful in sufficient quantities. These include cadmium, barium, cobalt, strontium, chromium, and in the case of some older orange ceramic, URANIUM.
Blue glaze is probably copper or cobalt based. I found a reference on ScienceDirect about high blood cobalt levels in association with lead poisoning from glazed Greek earthenware. This indicates that cobalt can indeed be leached out of the glaze and absorbed into the body. Cobalt is eliminated rapidly, but is moderately posionous, and copper is problematic in large quantities. Which brings this back to where I started: it won't kill you, and probably won't make you sick, but it's not really worth the risk.
File it in the same category as eating egg salad left out in the heat a few hours?
One other caution: prolonged contact with acid may damage and discolor your formerly handsome crock, in addition to leaching out these metals. To check for this, you can leave white vinegar in the container for a week or so, checking for change in color of the vinegar and the container every day.
In regards to your particular tomato sauce. I don't think its acidic enough (a pH of 4.6 that is), and according to this page - the answer is no. Even when canning fresh tomatoes or other tomato sauces you need to add some lemon juice. Now you could try lowering the ph, but it would drastically change your recipe probably - whether or not you want to do this is up to you.
If you have a pressure canner, you likely can do it.
Generally, yes - it is a function of temperature and acidity. You need to either sterilize the food through temperature, or create an environment in which the bacteria won't grow - normally a higher acidity. Pressure canners work by sterilizing, so recipes that are low in acid can still be canned.
Best Answer
Yeast eats sugar and makes alcohol,
Acetobacters eat alcohol and make acetic acid which is vinegar.
Both alcohol and acetic acid inhibit other microbes. Once your solution is alcoholic or acidic enough there is no risk of mold.
However- this recipe does not include any yeast or acetobacters, it relies on getting the necessary microbes from the air and the surface of the pineapple. During that initial period there will be a risk of some other microbe taking over and spoiling the batch.
Personally I would take out a little insurance and include a pinch of yeast in the initial mix.
If you have an old bottle of undistilled vinegar around you might have a colony of acetobacters (called a "mother") growing in it already. This wouldn't be necessary to prevent spoilage but would speed up your vinegar production greatly. You would add a piece of the mother after most of the sugar had been converted to alcohol. After your first batch you could use the mother in future batches.
This sounds like an awesome experiment and I'm going to have to try making some as well.