As to strengthening the left hand, I'd be very wary of such efforts.
The best way to strengthen the specific muscles needed for guitar is by playing guitar.
Since with a normal barre chord, only 3 strings are not fretted in front of the bar, dead strings can be caused by insufficient pressure, but just as often, maybe moreso, is that the other 3 fingers aren't clean over the intended strings. Instead, they are making contact with the 2nd or 6th string, which deadens the note above the barre.
One thing to try, is to play the minor chord not the major. This should help you keep that finger straight and firm, by leaving the middle finger angle to the next fret up moving the whole hand. When you can grab the Am barre every time, then try adding the major 3rd.
As to finger picking, I've seen lots of exercises online. I don't play much fingerstyle because I don't have the nails for UT, and I hate fingerpicks. I can do stuff like "From The Beginning", "Bron Yr Aur", "Blackbird", but that's a few songs out of the hundreds I know. Can't provide more help. I'd look for exercises in videos about classical guitar. Or flamenco. Those players are extremely diligent about accuracy & consistency so they probably come up with really good exercises.
One last thing: one of the things we can do on acoustic is different chord voicings. One example: instead of playing FM barre, try this: little finger on 6th fret, 2nd string (there's your F); ring finger a fret back, one string up (C); now, index finger 2nd fret, 4th string (F again).
When playing it, use the 5th string open to get the major 3rd. Just play the middle four strings. To add flavor and some edge, play the 1st string open, too. Gives you the major 7th. And uses those open strings which adds richness to the sound.
Now, you still get a 5 string, 4 tone chord with no barre. I mess around with inversions all the time.
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