Home made purees should be fine for a few days in the fridge. If I made a lot, I'd keep out enough for a few days in the fridge, freeze the rest, defrosting as needed.
If a spoon has been in baby's mouth and then in the food, that food should be discarded, not saved and reused. Babies saliva on the spoon will get into the food and can breed bacteria, etc. To avoid wasting food, I usually spoon a very small serving into a separate dish and then feed baby from that. If she surprised me and eats more than I expected I refill.
HTH