Don't crank down toooooo too much on the axle nuts. I did that once and assploded the spacers in between the nut/frame.

for one it keeps the chain from pulling the wheel towards you when your hammering on the pedals, and yes, they work great.

a chain tensioner keeps the axle from slipping forward when you're riding. I.E. your chain won't get slack if your nuts aren't cranked down tight enough. i don't use one, because i blow my ****ing tire out every two seconds, forcing me to retension my wheel anyway. but i think they're a worthy investment for anyone else.

Do I just need one for the side with the chain?

if my tiny bit of physics knowledge serves me correctly, yes.