Chinese Elm Bonsai help
I'll start like many others seeking help here by saying that I'm new to owning a bonsai, but I've spent a lot of time reading up on it. After about a week of struggle I've decided to turn for help.
I recently purchased a Chinese Elm bonsai off of an amazon vendor (which was probably a big mistake) and it arrived infested with pests. Right as I opened up the packaging I spotted a white grub and another slimmer brown grub-like insect. I killed the white one right then and the brown one at a later time (though no guarantee it was the same one). In the soil I also noticed small winged insects.
The leaves of the tree had some obvious issues from the start, which I attributed to the grubs - some leaves looked like they were cut, others had straight trails on them (images below show this).
I ran over to home depot and got some insecticide soap and showered the tree with it. I also plucked out most of the leaves that seemed to be affected (I noticed that the cut leaves would dry up after a day or two). As I was going through and defoliating my tree, I also noticed that some (small fraction, at the time) of the leaves had small black spots on them and seemed to be drying out as well. I also removed those.
It's been a few days since then and upon inspecting my tree closely today, I found that the black-spottedness has spread a great deal. Upon some research, I figured it's the black spot fungus. Though there are also some leaves with whitish spots; which makes me think I might have spider mites...
Here is a picture of my tree as it is right now:
There is a fair deal of new growth, though I might have overwatered it recently - some of the leaves are getting droopy.
At this point I'm not sure what to do. I'm considering repotting it or defoliating it further and applying some fungicide or both.
I'd greatly appreciate any input on what may be the cause of the problems and how I should proceed.