It should work fine unless the 2013 models have the newer style Magsafe adapter which has a smaller/thinner magnetic connector. Just measure the connector with a ruler and compare it to the pictures provided on amazon. I think they are 1.2cm by .5 cm. If it's the newer smaller size, LeexGroup offers one in this size as well, just make sure it's 85W and 18.5V.
It should. I purchased mine to work with a late 2007 model (it came with a similar 60w charger). Because of the thin cord design on these, I've went through at least 3 (both Apple and Generic versions). Here's something to prepare for: When I use Apple charges, I can use my machine right away, as soon as I plug in, even if the battery is dead. With the generic charger, if my battery died, I have to wait a good 10+ minutes before using my machine. I'm not entirely sure why, but that's been my experience just to let you know. I should also note that I only use the generic charger as a backup.