Was any Russian design feature incorporated in modern US fighters jets or vice-versa?
Three things come to mind:


Geometric shaping for stealth is based on the theoretical work of Petr Ufimtsev, a Russian mathematician who explained how to calculate the reflection of radio waves from the 1960s on.
The sight-controlled missile targeting which appeared in the MiG-29 in the 1980s. In combination with the wide off-boresight capabilities of the aircraft's radar and the missiles, it allowed to get a lock on aircraft flying actually behind it. When US F-16 met ex-GDR MiGs in exercises in the early 1990s, they were shocked to find how much superior the Russian design was and soon copied it.
The rotating collars which were used on the Yak-141 to deflect the engine exhaust straight down for vertical take-off have been used in the VTOL version of the F-35. Lockheed-Martin co-operated with Yakowlev in the early Nineties to learn how the Russian airplane works.


From a historical perspective you can add the Russian (actually, Georgian) aircraft designer Alexander Kartveli, who headed engineering at Republic, and the influence of Georgia-born Alexander de Serversky (actually of Russian descent) who propagated strategic bombing to win future wars, even though this concerns bombers, not fighters.