I'm rather new to playing the piano and reading sheet music. Because of this fact I want make sure that I understand this correctly and have been doing it right. Does the tie in the second measure tell me to hold that note until the second beat in the second line on this page? Also the chords in the bass clef of the fourth and fifth (and three more) measures have a line that seemingly breaks them up. I've been using this as an indication to play the notes above the line with my right hand. Is that correct or should I just use my left?!
The notation starting in the second measure, isn't a tie, but rather a slur. More specifically, it's a phrasing slur indicating to play everything within that slur as a continual line and within a single phrase. You only need to play that quarter-note A in the second measure for the duration of one beat.
And your intuition regarding the brackets in the chords is correct; that's telling you to play those upper pitches with your right hand.
A tie is always going to join two (or more) notes that are the same note. Usually across a bar line, but sometimes within the same bar. But always the same note pitch. Those lines would be way too long for ties! As Richard states, they are from the beginning to the end of a phrase. It's like each note is a syllable or word, and it's all said in one breath.
Again, as Richard says, and you guess, the lines join up notes to be played with the right hand. Easier than writing them in the treble clef; but only because of their duration.