There are budgie experts on here and I'm not one of them but I can hopefully give you a couple words of help that are not off the mark.
Yes, your little fellow is far too young to have been given away but, as you said, what's done is done. Thank you for taking care of him now...he'll need you!!
The baby formula is powdery and does need warm water....since he is older, if he is being spoonfed and not fed with a syringe down his crop, I don't think it is AS imperative that the food be the exact temperature. It should be warm, around 108, if I recall, but definitely NOT hot...NEVER hot. If it cools a bit while he eats it to the point where it is cold, you can always make a bit more. Microwaving can be tricky since there are hot and cold spots....you have to be careful that it is equally warm throughout. Some don't mind it when it gets a little cooler, others will refuse it...I think it is best for them to have it warm...goes down easier.
I believe that if the consistency of the food is runny, his droppings will follow suit. If it is thicker, the stool will also be more formed but I do believe they tend to look softer, in general, since the food is not hard. Baby budgie might still be young for veggies....others might want to weigh in on that. A good weaning food is quite nutritionally complete and since he is only a few weeks old, I'd stick with that for another couple of weeks...then start adding the veggies.
Hope others can help more....lots of wise people here.
