Regarding your F to G question.

There are so many ways to do it. You could "hammer", which is one pick stroke for the two notes. You could make a real conscious lift off the neck for of your index finger, or you could really have the space between the lift and the G be non existent. I play it such that I would leave my index on the G, as I like having my fingers on the neck as much as possible. It also depends on what the next note is, where I gotta move to.

Try to make sure you pick up and down. I taught myself to play guitar and I down stroke too much. I play a bit too much like I am in the Sex Pistols due to this.

Honestly I would focus more on chords than single notes at this point. If you just learn E, A and G, you can play a lot of songs. Playing songs will give you the fever.