I have tried this myself in the past through both the Facebook app and also going through Safari. I don't think I was able to do it and ended up doing it on my PC. That was a while ago, so perhaps with the new updates it has improved.
Regarding your question you can upload profile pictures from the iPad on Facebook. In the app in landscape press the tab which is 3 horizontal lines top left corner, the page will move to the right to reveal sections on the left. Press photos, select the photo you want, once it loads press the tab top right which is a box with an arrow and select Make Profile Picture. If you cant see the tab just tap top right and the tabs will appear. I'm assuming you already have photos on the app if you don't once you select photos press the + tab top right and you can take a photo, select from your camera roll or create an album. Hope this helps.
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