How to add fruit puree into yogurt without making it too liquid?
A great way to add fruit to yogurt is to use a jam, jelly, or fruit preserve of choice. By cooking out the liquid and thickening with sugar and pectin, a jelly ends up much less watery than a fruit puree. Depending on the fruit you are starting with and the desired texture, the exact recipe will vary. Store-bought jams work as well.
If you are looking for a fresh fruit flavor (as opposed to the cooked flavor of jam) you still have a few options. You could change the composition of your puree (e.g. by pureeing dried fruits, or choosing a less watery fruit to begin with). You could add a thickening agent that activates without cooking, like pureed chia seeds.
Finally, you could keep your puree as is and use a thicker yogurt: greek-style or another strained yogurt should be thicker in the first place, and the texture should still be reasonably thick even after mixing in a watery puree.
I am not sure how to answer your preservation question. A mixture of fruit and yogurt should keep decently in the fridge. But if you are trying to preserve it longer, we would need more details about your process.