That fighter jet is a dead ringer for the F-14 Tomcat.
No it is not. (No swing wings, among other things...).
It is, however, a dead ringer for a Su-27 or Su-30 from which it is licensed or copied.
Their new J-20 Stealth fighter surprised a lot of people. No match for the F-22 yet, but a lot better than our own analysts expected at this time...but it is not a naval fighter.
In 2011, the PLAAF conducted a test flight of their new stealth fighter. As there has been a lot of speculation and comparison, here are a set of images comparing the USAF F-22 Raptor (which has been capped in production at 195), with the PLAAF J-20: