7th sus4 chords
The seventh suspended chords are less common than the regular sus4 and sus2 chords, but not that seldom. As with sus-chords in general, the sus7 chord is often almost similar to the dominant 7th chords, but in many cases the shapes are kind of hard to play because of the lack of natural ways to add the fourth tone.
The diagrams below are suggestions of how to play these chords.
The C7sus4 is obviously a barre chord, it could also be played as X33311, with a two finger bar on the first fret plus a stretch to the third fret. The most common alternative to the suggestion for F7sus4 is to play it as a barre chord: 131211. This is also true about G7sus4.
Yes, this chord type also exists, but since they are much more uncommon than 7sus4 they are not present on the site so far.