i am teaching kids. I learned some tricks to help.
Everybody finds switching between chords hard to begin with. Two things that help.
1. don't rush. play the song as slow as you need to to have enough time to switch between chords. Slow down the rythym of the song.
2. dont worry about the strumming hand. Do some exercises where you place the fingers on the chord very lightly, and then do 'reps' of pressing down. This trains your muscle memory to get used to getting all fingers to make the chord at the same time. Often people will move individual fingers. Neuroscience FTW
As for the F chord. There is a version that is not barre.
But when I was learning, I did not know that, and I was forced to learn the barre version. However it was then when I started really making progress. Barre chords is a significant milestone and puts you in a category where you are already better than lot of guitar players.