First off, welcome to the forum. Typically kit instructions fail at their fermentation procedure recommendations. They usually give generic guidelines like, keep in primary for one week than transfer.
15C is fine, in fact, well within the 9-23C guidelines listed by Fermentis,
www.fermentis.com/wp-content/uploads/2012/02/SFG_S23.pdf. Keep in mind that the guidelines are referring to the temperature of the beer, not the ambient temperature. Typically, fermentation raises the temperature of the beer a few degrees higher than the ambient temp. This is more pronounced with ales than with lagers in my experience. Still, you'll be in the yeast's temperature range.
You'll read in Palmer's online How To Brew about diacetyl rest for lagers. I would say to sample the beer as fermenation appears to be winding down. If you taste a buttery, diacetyl flavor, then do the diacetyl rest, if not, I would skip that step. I've heard several prominent homebrew figures like Jamil Z and Gordon Strong speak about not doing a diacetyl rest, I've also heard from good brewers in my homebrew club about this approach. I'm trying it myself for the first time with a doppelbock I have fermenting. Once fermentation is complete, for a lager, probably about 3-4 weeks, (once the gravity readings are stable over a period of several days), you can then cold crash, or move the beer into a secondary vessel if you want it to clear up and give the beer time to lager/bulk condition.
I hope this helps