If I did the ATPL theory exam now, would I have a time limit to finish the ATPL? If so, what is it?
And what about other EASA licenses, CPL, (E-/CB-)IR, etc.?
Generally you have 7 years for your ATPL theoretical knowledge, but actually it depends whether you already have Instrument Rating and Commercial Pilot License. If you do not have CPL and/or IR, you have only 36 months. If you have IR, you have 7 years.
Moreover, according to FCL.025(c), you have to pass your IR in 36 months after the theoretical exam (nevertheless, IR or ATPL), and then, if those exams were ATPL (I believe that you are going to pass ATPL without separate IR and/or CPL theoretical exams), your theory will remain valid 7 years from the date of your IR.
For more information you can refer this document, part FCL.025(c)(1) and FCL.025(c)(2).