Is getting a dental implant post removed painful?

No. You would expect similar post operative symptoms related to removing a tooth. Post operative pain is related to the pre-existing condition of the failed implant or tooth. In general, the average patient has minimal post operative discomfort. If you are referring to removing an implant abutment (post?), there is no pain associated with that since it resides inside the implant .
Implant removal. If the implant is failing and partially integrated (fused to the bone) and needs to be trephined out (drilled away from bone connection) then yes you can indeed experience some pain and swelling post-operatively.
Normally not painful. It certainly depends on the nature of the situation, but techniques of implant removal have evolved, and in the majority, but not all procedures can relatively uneventful.
Usually Not. Removing a dental implant is essentially not much different than removing a tooth. Matter of fact, often it's quite easier, due to bone loss or fibrous tissue integration which has necessitated its removal in the first place. I wouldn't worry about it. If you've done fine with the original implant surgery, you'll do just great! keep smiling friend !
Variable. If you are sufficiently numb, it is not painful to have it removed. Healing afterwards can take some time 7 - 10 days before you no longer are very aware of it. Usually 5 - 7 days of sore gum tissue is about it.
Not Usually. The discomfort is comparable to having a tooth extracted if the implant is a standard root form implant. Older implant types such as subperiosteal implants and blade implants require significant surgery and have a much longer recovery because of work involved in removing them.
No. After receiving some anesthetic ( like going a filling). There should be no pain, maybe some discomfort. Many times you can the implant removed , area cleaned out and a longer implant placed the sanme visit to avoid another surgery visit.
Not usually. Usually dental implants, which require removal, are loose or present with deficient bony support and may be removed simply by backing out the implant. There are cases in which the implant requires a trephine bur to remove or loosen them. It wont' be uncomfortable with adequate anesthesia however, there may be significant post-operative discomfort. Pain meds can alleviate the discomfort.
Pain from infection. See your surgeon who put the implant in and he will be able to see the problem. As a general dentist I have not seen any pain from implants.
Depends. Depending upon the situation that warrants it's removal and how secure it is in the bone there could be some discomfort following its removal.