Hi everyone,
I recently purchased a healthy-looking Indian Summer Crabapple tree from Lowes. Since planting it (3 weeks ago), I have noticed that a lot of the leaves have developed orange/red colored spots. Being new to gardening, I did some research online, and I think that this is likely Crabapple rust. Does my ID seem correct?

I have sprayed the leaves with fungicide, but it continues to spread across the leaves. I have noticed, however, that it doesn't seem to affect the new leaves. Once these leaves become a week or so old, however, and switch from their original purplish shade to a greenish hue, they do often present those orangey spots. Are there any steps I should be taking to protect my tree?

I simultaneously noticed that some of the new leaves, and in particular, those growing closest to the main trunk of the tree, are rapidly turning spotty and then fully yellow before falling off. Is this an unrelated problem? We have had a lot of very very heavy rainfall in Northern NJ in the past week so I am wondering if this is simply due to overwatering, or if it might be some other issue.

I have attached a few pictures which detail both problems for reference, and would appreciate any feedback and advice that you can provide.

Thanks!