Hello,
I am quite a beginner at this so sorry if I did something wrong. Last year I have got this bonsai as a gift. I grow out nice and healthy (last picture) but then it got `Tetranychus` so I got a spray for that and it turned out better. Until recent days it was good but for an unknown reason to me the leaves started to fall and I noticed these small black dots on leaves and second thing is that the leaves are not as green as they were before. I started fertilizing recently. Can anyone suggest what can I do with this and for a second what bonsai is this (was never told the type)?

First it is indoors. , It looks like it might be an azalea, if it is then it will not survive inside, as you have found out. Not convinced it is azalea, but I am sure it should be outside. You need to make sure you are watering properly, and right now I would remove the flowers They are not doing it any good.

If you had spider mite then the plant is suffering from being in too dry atmosphere, but the mite has done a lot of damage and the plant is weak.