Chinese elm problems - please help!

[Zelekolac]

Hi.

I bought an indoors chinese elm about 2 months ago. I did my research on it and noticed right away that the soil and the pot were not right (there were no draining holes) and that there were different kinds of bugs crawling in the soil. To prevent the bugs from spreading to my other plants, I put the elm outside until I would repot it. And I did repot it about a week ago.
When I took the bonsai out of its pot, a large amount of leaves fell off. Before I put it in the new soil, I soaked it in cold water for about 15 minutes. Once it was freshly repotted I watered it and sprayed the leaves with an insecticide called Biokill (that's because it used to have mites, so this was done as a precaution). Since repotting I have watered it once (the soil is always moist). It's now indoors and on a well lit windowsill with good air circulation.

So my problem is: the leaves keep falling off. I understand that this sometimes occurs in chinese elms, but I can't help worrying. Some leaves fall off completely green, some yellow, but the majority of them is a mixture of green, yellow and black/dark brown spots on the edges and sometimes on the whole leaf. The leaves that fall off are very dry but almost never shriveled. The leaves fall off no matter if they are old or newly grown.
I am worried that these black marks might be fungi, or maybe that I caused some sort of damage when I sprayed it with Biokill (even though a saleswoman in a gardening store told me to do so), or maybe I shouldn't have soaked it in cold water? Note that this is my first bonsai tree and that bonsai growing is not very big where I live, so I don't have many people to turn to for help. Can this just be a normal occurrence because of the repotting and winter nearing? I'm worried that the tree won't recover.
I will be very grateful for your help and any tips on how to take better care of my bonsai.

[Zelekolac]

Thank you for answering David. I actually found out today that it's a fungal disease called black spot and I am now properly treating it. I will keep your advice in mind in case my bonsai has any further problems.