shabbos

Question

It seems from your answer about being in a car on Shabbos the problem is two-fold. 1) Amira L'akum and 2) Techumim. If that is the case can one catch a ride with his non-jewish neighbor who is going out shoppping anyway (adayta dnafshey Avid) and is inside the Techum. Can one catch a ride on a bus as long as prior payment arrangements have been made and I will not be traveling outside the Techum. Also what should one do if they went to a hospital on Shabbos for Pikuach nefesh or other reasons that were permissable and has been released? should he stay in the hospital the rest of shabbos or can he have a taxi take him home?