A LAND SURVEYOR'S THOUGHTS:
The above posts describing the map calls as bearings are correct, they are not LAT/LONG coordinates. The bearings are normally relative to some definition of North. Sometimes that is from an old legal description or nearby plat, sometimes it is magnetic, astronomical, or even assumed. To a surveyor North is relative for any individual piece of property and true North is generally not that important. If two adjacent properties are examined, then one properties bearings can be rotated to match the other by subtracting the bearings on a common line.
The best use of a handheld GPS would be to use it as a compass in conjunction with a measuring wheel or fiberglass reel tape to get to the next point. Using a hand held GPS for line clearing is probably a bad idea. If you assume your handheld has an accuracy of 20+/- feet and the known section of the line is say 400 feet long, if you were to extend those coordinates with the GPS another 400 feet your accuracy drops to 40'+/-.
Averaging a handheld GPS over a point for a long period of time is pointless. The largest error with any single GPS unit (without the benefit of RTK corrections) is due to atmospheric conditions. No amount of averaging is going to compensate for this.
The T&R system is called the Public Land Survey System. To my knowledge, the PLSS exist in most parts of every state except some of the original 13 colony states. The surveys of the public lands divided states into township (usually 6 miles square and were designated by town/range) and divided the townships into normally 1 mile square sections. Metes = direction & distance, Bounds = layman call such as trees, fences, adjoiners deeds, etc. Some descriptions are written metes & bounds off of the section's corners and some descriptions are written to fractionally divide the section into halves, quarters, etc. Descriptions for states that do not have the PLSS are usually written Metes & Bounds off of some known control marker.
CODE54 as long as you and your neighbors agree on the corners then there should not be a problem, but not all banks require surveys as part of a typical home closing. Their only interest is that there are not any major encroachments or deed problems that would affect the value of the property. This can be checked WITHOUT a survey. Surveyors are the only professionals that can accurately translate a legal description or plat map to the ground. There are no other governmental or other agencies that can help you with that unless they staff surveyors & survey records. Even so they won't do it for free. Around here $1800 would figure for about 2 full days of a 2 man crew to work in the field plus some research, computing, and drafting time. Surveyor's GPS does not work well in the woods (and not everybody has it) and so the survey might have to be done using line-of-sight methods.
I field several calls a day with the same questions you are asking. They are good questions, but the answers will probably very depending on your specific location. Your best bet is talk with your local surveyor.