When serving a straight line should be held through the shoulders and the hitting arm elbow, at least this is what I have gathered.
A serve motion is not necessarily held. I dont like the word "held" for the serve motion because it sort of implies something stops. The line you are referring to shapes the body for an upward rise through the ball that also goes forward to the tossed ball. What this is loosely trying to say, is you dont want your body shape to be largely parallel to the court. But on an upward angle. Here is your example video.
http://www.youtube.com/watch?v=Kpj5ZthpxbI
But should the forearm and wrist remain completely flexible? I know that a relaxed hitting arm is key to a good serve but HOW relaxed?
It needs to be REAL, REAL, REAL relaxed. So relaxed, that I could pull the racquet out of your hands with two or three light tugs. There should be little pressure on the handle THROUGHOUT the serve motion. You only want enough pressure so the racquet doesnt fly out of your hand. You can find this out by testing it and learning what the limitation is through practice.
Your shoulder area needs to be completely relaxed. Many players do not have a loose relaxed shoulder when their racquet drops and their hitting arm starts to extend towards the contact point. You want this area real loose because your non-hitting arm folding into the body is going to help with accelerating this arm. Your momentum and body braking is what accelerates a loose hitting shoulder and arm, not your shoulder muscles. Once they tighten, flexiblility is diminished.
and then start the swing that the upward movement creates the racquet head drop but it seems that this makes the movement of the racquet a little unpredictable and can cause some strain on the shoulder.
Not really. The racquet head is only unpredictable if you have a snag or a hitch in your motion. If you attached a ball at the end of a 4' rope, and swing it around and around, you should be able to control the balls flight path. The same is with your racquet head.
I tend to make the racquet drop a more conscious movement rather than just letting it happen. Am i doing this correctly or is detrimental to my game?
That is faulty serve thinking. The motion of the serve is continuous. It does nto stop and the braking that goes on throughout the kinetic chain slows down and accelerates different parts of the body as it works its way up to contact. This is continuous. The only thing you should be working on in your thoughts is to completely relax the hitting arm throughout the motion. In fact, I dont even want you to think, it is something you just do or release. This is difficult to do because subconsciously our muscles fire and of course tighten in the process thinking they have to do something for whatever reason.
For the serve motion, this hitting arm needs to be completely relaxed. Your thoughts need to be towards relaxation and fluidity. And because we tend to tighten our muscles during movements, you need to train yourself through practice to relax the hitting arm and shoulder in th serve. It is not something people just "get."
As for the grip, the strength in the hand largely comes from the pinky and the ring finger. If you try to grip something without those two fingers, your hand strength diminishes. In order to promote relaxation throughout the swing motion and especially in the hand, try and keep the pinky finger off the handle. That way if there is slight pressure applied to the handle at contact (which is many times done subconsciously), it wont be too much and you can better control the amount of relaxation needed.