Had spleen removed laparoscopically almost 3 mo ago due to itp. I still have some pain and tingling mostly near my navel. Is that normal?

Healing pains. You had your splenectomy performed by laparoscopy. It may have been multiple small holes or a single port at the umbilicus. The doctor morcelized the spleen in a bag to remove it. If you are 3 months after then the pain may be from the nerves growing back at the site. As long as no drainage or redness then continue to observe. If it is hot, tender to touch, or draining fluid then call.
May be. Normal to have temporary skin hypersensitivity at a surgical scar for several months. See your surgeon for an exam if you have concerns.
Yes. You may have minor symptoms like that for a couple of years. Many small nerve fibers are cut in an operation like yours and they grow back very slowly. But it will be fine in the end.