I agree with Dave, you should probably see a tax professional.
To answer your questions, though, I submit;
Either one or the other (not both) of you should be able to "claim" the allowed expeditures if both names are on the property.
Since you are not filing a "Joint" return, there is not a problem with whomever claiming the property itemizing. Normally, if one person itemizes (as in a married couple), it is necessary for the other to also itemize. You and your girlfriend do not have to deal with that problem.
As to whether or not it is worth itemizing, that depends on whether or not your itemized deductions are more than your standard deductions.
With the above having been said. I would still encourage you to see a tax professional who can really see your TOTAL situation.
Do the right thing!