Should one maintain a constant attitude if he wants to hold a constant speed or does the attitude vary depending upon the wind direction?
If by attitude you mean pitch attitude or angle of attack (which is how I automatically understood this), no it does not change as this is related to the aircraft's airspeed through the air. So an aircraft flying downwind will have the same AOA as the same aircraft at the same airspeed flying upwind.
If you want to fly at the same groundspeed upwind as downwind, then you would have to vary your airspeed, which means varying you pitch attitude or AOA. This might not be possible if say you were in a light aircraft in a 40 knot wind at altitude which cruises at 100 knots.
Yes. Constant pitch, constant airspeed. "Pitch plus power is performance, pitch for speed, power for altitude."
Wind affects groundspeed, not airspeed (except for sudden gusts or sheer).
Unless an aircraft has landed or is fastened to the ground, like a tethered balloon or gyrocopter, an aircraft is always moving along with the wind. Think of an airborne aircraft as being one with the wind. Wind exists only from the earth's perspective, it has no affect on a flying aircraft. Except...
Wind does affect heading and groundspeed and becomes important when navigating relative to the earth. It's especially a factor in landing and taking off!
So, yes. Constant power, constant attitude will result in constant airspeed, no matter what the wind down on the ground is doing.
The lift generated is proportional to the airspeed and the angle of attack (amongst other factors).
If the wind direction changes, the aircraft will maintain a constant airspeed, by increasing or decreasing power. To maintain level flight, by maintaining the same lift, the angle of attack, for the given weight and altitude, will remain constant therefore there is no attitude change.
If the change is in direction, the airplane will change its yaw (also known as heading) angle, so that the track angle (the direction along which it is travelling) does not change.
For more informations about the differences between heading, track and similar angles, you can read this other question.