I have gestational thrombocytopenia @ 35 weeks platelets are 102. Will I be able to have epidural?

Yes. Typically anesthesiologists will give an epidural as long as the platelet count is above 75k. Depending on the doctor, some are more comfortable with higher or lower values. Giving an epidural when platelets are very low increases the risk of bleeding in the spine which can cause serious complications. Your platelets will be rechecked when you are admitted to the hospital.
Possibly. Specialists have different comfort levels in whether or not to place an epidural. Most would not place one at 50k or below and between 50 and 100k its a judgement call. You might want to see a hematologist or high risk OB specialist to see what can be done to keep your platelets over 100k.
You will have . To have your platelet count redrawn prior to the placement of the epidural. We look at two things, absolute number of platelets and the downward trend. 102k should be fine, but if there is an acute significant drop, that may increase your risk. Also, if your platelets fall below the 70-80k range, you may also be ineligible.