From this question, it is been suggested to ask different question, rather than keep discussing it under comment section.
First thing first, let's go over some concept: heading is which way the plane's nose is pointing at, track is which way the plane is travelling on the ground. E.g. if your heading is 360 (North), and the wind is blowing from 090 (blowing East to West), the plane's track may be 350 (slightly left of North).
With that in mind, it's not hard to deduce most of the time pilots want to fly track, rather than heading. The purpose is to navigate from point A to point B on the ground. In our example, you have to turn the plane slightly to the right to compensate for the crosswind. To figure out exactly how many degrees to turn, you will first need to decide how fast you want to fly. After that, it's simple geometry.
A mechanical flight computer can be used to calculate the drift angle easily. Using it is a matter of marking dots on a transparent disc, then sliding and rotating it to the correct position and read off the pre-calculated figures below.
If you are flying manually, or flying a plane with an elementary autopilot, you will need to calculate the drift angle, then add (or minus) that to your desired track to get the heading. You will then set the heading bug to that value. Theoretically, that heading should compensate just enough crosswind that you stay on your desired ground track. In practice minor adjustments are often necessary. Provided that the numbers you use are not awfully off, you should end up with an estimation good enough for the safety of your flight.
If you are flying a plane with an advanced flight computer which has the ability to detect winds aloft, your autopilot will fly the track you dial in and automatically compensate for crosswind.
So to answer your questions:
You will use simple math or tools to compute the heading which will let you fly the desired track.
It does not matter when you have an exact headwind or tailwind.
Heading bug denotes the desired heading, not track. You always turn your plane towards the heading bug.
Advanced autopilot fly track, fundamental ones fly heading. Some autopilots can read the heading bug position on the instrument, others must be set explicitly on another panel.
A) Divide the wind speed (in knots) by your NPM( nautical miles per minute). This is your Max Drift. B) Use the watch face to determine how much of that Max Drift you need to use: 15 is a quarter of an hour, so for 15 degrees you use 1/4, 30 degrees you use 1/2 of Max Drift, 45 deg 3/4 and for larger degrees use the hole Max Drift
eg. wind 230/45 , your speed 180 kts (or 3 miles per minute), hdg 270
Max Drift = 45 / 3 = 15 degrees
Angle between wind and me : 40 degrees, so I use a little more than 1/2 and less than 3/4
(between 30 and 45 on the watch face)
Computed Drift = 10 degrees
Set Hdg Bug to 260 to keep track 270
Hdg bug will not be affected by tail wind, but your ground speed and ETA will be affected. A CRP or an apropriate app sheet can tell you by how much.
It will matter if a) wind is very strong or b) your navigation leg is long enough (30+ mins)
Depending on the sophistication of the autopilot, most of them have a "keep heading mode" where the a/c will maintain the heading selected by the heading bug. If operated in that mode, the pilot can turn the a/c by moving the hdg knob left or right.
To track a course in a crosswind using the bug, set the OBS to the waypoint you wish to fly to and use your normal crabbing skills to track the needle (025 below). Once the needle is being tracked, you can set the heading bug to the current heading (015) and just fly that. This works with or without an autopilot.
