Taymoor,
On the upper body movement, what often works for folks that I help is to use a mirror so that you can see what you're doing. Don't get absorbed into using one, but drawing facing and perpendicular to it so you can see what you're doing and limit that movement will help.
Break down your drills since you're starting out. Here's a routine:
1 - With full grip acquired, gun at low ready, bring the gun up and present to the target. Do that about 100 times until you can do it perfect and the sights are perfectly aligned on your target (dot on the wall, light switches, etc. are good for this).
2 - Strong hand gripping the pistol, weak hand off, acquire grip and present the gun to the target. Again, do this until sights are perfect.
3 - Pistol resting in the palm of the weak hand. Acquire the pistol with the strong hand, grip and present. Yep...do it 'til it's perfect.
4 - Pistol on the table. Pick it up and acquire your grip and present 'til sights are perfect.
If you need a stamp of approval, this is what Brian Enos did when he was starting out.
To speed the draw, the best advice I got was to simply....GO FASTER! Like Jesse was saying, you want to initiate the draw at the beginning of the tone of the timer. If you wait 'til the timer has completely beeped, you're already down at least 0.5 seconds. A good way to work on speeding up reaction time to an audible start signal is at the range. Set your timer to random start. Pistol load and gun up on target. Fire a round at the first tone you hear. Max Michel says, "listen for the 'B' in BEEP".
Getting the Burkett videos are a great resource for pistol technique and practice tips, but nothing will shorten the learning curve than attending a class from one of the top shooters. Max and Travis are pretty affordable. You have Strader in your area. Matt Burkett and Mike Voigt are AWESOME to train with and Dave Re would be another person I can recommend.
Rich