in example 1:
Treat the grace appoggiatura note, B as a quarter note, the following note A is then held for the rest of the measure - (for the remaining 2 beats).
Ignore the bracketed note. Ignore the lines written by hand.
In example 2:
offers alternative fingering for the A.
In example 3:
Again, alternate fingering is offered. Choose either the top fingering or the bottom.
In example 4:
Your left hand is playing 2 'voices'.. No big deal. Hold the D for the whole measure; on Beat 3 (hence the 2 quarter rests) play the f# while still holding the D.
The random line is to remind the player to hold the D while playing the f#.
PS... Thanks, Ryoutak. (I'm guilty of being loose w the term). Yes, the proper term is appoggiatura - 'grace' being too generalized a term here.
The appoggiatura is always worth 1/2 the amount of the note that follows. However, in this case. that would have you striking the 'A' on the & of 2.. which would sound a bit off. Originally I had indicated to treat the appogg. as an 8th note, (realizing that 1/2 amount wouldn't quite seem logical), though now, I think the quarter is best for the value of the appogg.