I would explain palm muting a little different. Palm muting is basically self explanitory. You use the palm of your picking hand to mute the strings. You can achieve different palm muting sounds by applying more or less pressure and being closer or farther away from the bridge. however, applying too much pressure or being too far away from the bridge can change the desired pitch.

One thing I noticed about the tab you posted was that is was in dadadd tuning instead of standard (eadgbe). So, if you were trying to play the tab you posted and it doesn't sound right, that's why. Like iiholly said, you play from left to right and the line at the bottom is the low E string going up to the high e string.

Personally, I would get comfortable with changing from chord to chord with "regular" chords before I jumped into bar chords, but that's just me.