Can I use a tart pan instead of a springform pan?

Even if it is deep enough, the ridged edge of the tart tin could cause a messy finish to that crumb crust. I'd use a cake pan with a removable bottom before I'd use a deep tart pan. ;o)

it depends on how tall your tart pan is, and whether it has a removable bottom; if it's at least 1.5" tall (with the same diameter) and has a removable bottom I'd say go for it. If it's shorter, or doesn't have a removable bottom you might run into problems with overflow or messy slices but if these might not bother you.

Depends on the depth of your tart pan. Some have walls 2 - 3" tall. If you're using a traditional tart pan, you're going to end up with a lot of ingredients left over. If you do have a tall tart pan, I would recommend building a thin crust all the way up the side. A removable bottom and an expandable collar don't really operate the same way. Especially with tart pans, which often taper.

I think it might be risky to substitute a tart pan because it isn't as deep as a springform pan. From the photo, the cake appears to be taller than a traditional tart.