"the pattern says to cast on 177 stitches, so the 1st st and the 177th st on each row are to be kept in st stitch?"
"So what do I do about the pattern chart, which uses all 177 stitches for the pattern? ...the odd rows (1, 3, 5, 7, 9 and 11) are RS rows and begin and end with a purl stitch. The even rows (2, 4, 6, 8, 10, and 12) are WS rows that begin and end with a knit stitch."
This is simply 'reverse stockinette.' Work the selvedge sts as per the pattern chart.
"The sleeves are the only pieces that may be problematic as the odd rows begin and end with a k1tbl. What would I do there?"
Are the sleeves knitted flat or in the round? Doing a k1tbl simply twists the st. This creates a slight visual variance (especially if the piece is flat and the st in the middle) and tightens the st a bit.
"it says to BO x number of stitches at the beginning of the next 2 rows. Do I include the selvage st as one of the stitches to be bound off?"
"After I bind off the specified number of stitches on a row beginning with the selvage stitch, does the next stitch become the selvage stitch?"
In theory, unless you are specificaly told not to.
"Or do I just work that in pattern as the chart says to?"
Again, if you are told to.