Open F tuning
The open F tuning is an alternate tuning that involves both increasing and loosening strings in the retuning process.
You should be aware that this tuning put some extra pressure on the guitar, since two of the strings must be retuned in a way that increases the tension on the neck. Notice that it doesn't work with an Open D tuning combined with a capo on 3rd fret since the tunings are not symmetrical. But you can use a capo on 1st fret together with a E Ab B E B E tuning, which will emulate F A C F C F.
To get the open F tuning on your guitar you tune it like this: F A C F C F.
Including an octave perspective, the tuning is written F2-A2-C3-F3-C4-F4, meaning that the lowest string is an F note on the second octave, the second lowest string is a A note on the second octave and so on. Standard tuning reference: E2-A2-D3-G3-B3-E4. For tuning to F major with a spider capo, use a 100011 configuration against an E A C F B E tuning.
The Am7 doesn't include the fifth. Dm can be played with the root as the bass note as XX2420.
Some alternative fingerings:
More chords in this tuning:
Fmaj7: 004400 / 004000
C7: X34205 / X3453X
Obviously, more chords can be played by laying one finger over all six strings in this opening. There are more options:
C5/G: XX7777 / XX777X
The Fmaj7 doesn't include the third and can be written Fmaj7(no3).
These are only a few of numerous ideas for voicings when you tune the guitar as F A C F C F.
Progressions in this specific tuning:
F5 - Fsus2 - Bbadd2 - F
Bb/F - Fmaj7 - C/F - Dm7/F
If you want to go more into depth of this particular guitar tuning, see the Essential Chords in Open F Tunings ebook with over 200 chord diagrams.
This was an introduction about chords in Open F tuning, see also Open E tuning and Open C tuning.