You're correct about the ornament in green: the 5th fret note (an E) just before the 7th fret note (an F#) is called a grace note, and it is to meant to be a very short note played in anticipation of the main note (the F#). How short is "very short"? That's up to you.
As for the indication in red: the 'g.' indicates a glissando, meaning a slide from the first note to the second one, with all the notes in between included. In this particular piece, what you should do is slide from the 7th fret on the G-string (a D) down the G-string to the 4th fret---but just as you get to that 4th fret, you'll do a few things simultaneously:
- play the E-string, 3rd fret (which is a G). Unlike almost every other note, the music doesn't suggest a left-hand fingering---I'd suggest using your middle finger (2).
- let go of the G-string
- play the open B-string
You could both let go of the G-string and play the open B-string in one movement by flicking your ring finger (the one sliding down the G-string) off the neck in such a way that it plucks the B-string on its way off the G-string. But that would also probably cause the G-string to ring out, so you'd have to mute it with a free finger---I'd use my left-hand index finger.
This all sounds very complicated, but it's really not so hard with a little practice. Best of luck!