Do you have any pics of the links? Depending on the kind of bushings it has, it may not need to be greased. Of course, if you got zerks for it, I would think they would be greasable and their overseas manufacturer is just lacking in the QC department.
The rear sway bar links are designed to be installed on the outside. People only install them on the inside IF they are still running factory wheels without wheel spacers and to do that, you would need to drill new mounting holes. Not something I would recommend.
You need to just remove the brake line from the axle mount and run it over it like 2007-11 JK's came.
This write-up was written for 2007-10 model JK's and the removal of the automatic transmission skid plate would have provided enough clearance of the front drive shaft to make the installation easy. The new placement of the 2012-up exhaust crossover will get in the way of your drive shaft regardless if you have an automatic or manual and disconnecting it from the front axle should be done to all for full droop. There are only 4 bolts to remove and a 15mm socket is all that you need. This is a much easier and safer way to go than to use a spring compressor.