I need to get the Heal Others spell so I can get a mercenary and be able to heal him. Ive been looking all over the Temple in Mournhold (seems like the logical place) and can't find anyone who sells that spell. Where can I get it? I sure hope I don't have to go back to Vvardenfell just to get it.

And what about the beggar outside the temple. He claims to be an entreprenuer and asks for 50 gold, then another 100 then another after that. Will he reward you later or is he just taking your money?

Another approach is to give the mercenary Restore Health potions, although I'm not sure if he uses homemade ones or not. As for the beggar...be prepared.

look under the threads about gaenor if you want to know about the beggar though I can't protect you from spoilers if you dothat sirah

There are only five spellsellers in Mournhold but if you have to go back to the mainland you can use recall to return to Mournhold.

The spellsellers are:-

Laurina Matia and Crito Olcinius in the Imperial Cult shrine in the Palace; Nerile Andaren in the Hall of Ministry and Galsa Andrano in the infirmary, both inside the temple. And Mehra Helas who is walking around outside the temple entrance.

I'm afraid I don't know what spells they sell.

IIRC, they also have Spellmaking service. Use that to make whatever magnitude Restore Health (on Touch or Target) you want.