The browning is quite likely to be just shock from a change in environment. Different light (too sunny), humidity or temperature. Plants growing in an environment adapt to it and can suffer when the environment changes suddenly. You chose a pretty tough customer for someone somewhat new to plants. These plants aren't the easiest things to grow, they are fussy about light drafts etc. I am not an expert on Calathea, but know they get a few leaf spot diseases. You can take samples and send them to your local extension service. It is somewhat pointless to treat with fungicide if you don't identify the problem. A fungicide that kills one fungus can have absolutely no affect on another. The bugs could be White Fly or juvenile leaf Hoppers but without Pictures of the bugs it is hard to tell. Look these two up on the web and see if they look like one of them.

Thanks for your response. I don't think the bugs are leaf hoppers or white fly because what I have is extremely small. It's barely visible to the naked eye. Therefore, even if I took a photo of the bugs, you would not be able to see them.