I'm completely new to working on cars in general and just got my Mini, I was looking through the engine bay and discovered that this cylinder thing is leaking, but again, complete noob here and have no idea what it is called in order to even begin looking for how to fix it. Any help would be appreciated!

 

what you got there is the classic fluid motor mount leak

if you have warranty coverage it is time to meet your dealer

if not I'd recommend researching the TSW mount and a local MINI mechanic

 

TSW is a solid rubber (actually Urathane) mount that replaces the OEM one...it makes a bit more vibration...but lasts longer...
The OEM mount is about 85$, and will last a couple years...and will fail again someday....replacement is supposed to be pretty easy...but it does need some special tools.....

 

Thanks for the quick responses. I suppose I should take comfort in knowing that it is a common problem. I'll do some research on that TSW mount and go from there.

 

The only special tool you need for the motor mount is an e-torx socket for the long as bolt underneath that holds it in. Otherwise just standard mechanics tools.