Service road; posted speed limit 45; signal comes to red; two lanes and a marked shoulder. All incoming traffic comes to a halt for the red light, driver A gets into the service road from a shopping complex--first to the right lane and on their way to the left lane, having both the drivers on the right and left lane let them on to oncoming traffic. Lone behold driver B (traveling at 40+ mph coming to a red light) hits  car A (Car B had been traveling on shoulder, trying to pass other cars so Car B could stay a few cars ahead of on red light). Car B finally realizes there's already a car on that lane and they should move off there and in this process Car B hits Car A damaging pretty much all of the Car A's front bumper while Car B sustains only few scratches. Who's at fault?

Car B.

Not sure if I got the lane deskription right but I agree, car B seems to be in fault, because:

1. Car B was driving in the shoulder, not legal, and trying to get in the driving lane.
2. Car B changed lanes and most probably hit A in the middle (T-bone style) or back. In most instances, the one who hits from back is the culprit.

Two lanes and a marked shoulder; marked shoulder opens to left-only lane about 30 yards down do she was trying to pass few cars so she could stay on left turn where I was getting in (from shopping complex) after having cleared by drivers on right and left lane. She was trying to squeeze in to the left lane from shoulder.

What state? It's illegal to pass from the shoulder, which is what she seems to be doing, in most state.

Update

So after trying to call the other party's insurance I was able to get hold of them and she took a recorded statement and after 5 minutes of the recording she's saying I am at fault that I didn't yield to incoming traffic (whch is false). She also sent a letter stating that. So basically she didn't want to listen to me. She didn't even say that they will investigate, look into circumstances and decision. I am not happy with it. How do I fight it?

Small claims court if you think u r right by law, if the damage n price is big get a lawyer(if you have time) if not just move on..accident happens. ,,i don't think you ll get a specific answer here based on your scenario. If you are in TX call this guy Texas hammer,,i see him in the TV and have heard from few guys.

They need to disclose a disclaimer of recorded conversation prior to recording a formal communication over the phone. It cannot be used against your in the court of law.

Which they did

Contact seems to have been made as a result of A's persistence on not yielding to car B assuming A was in motion (front bumper of A completely damaged as opposed to side taking a hit). If A was not in motion, then it is entirely B's fault.

http://www.insurancebrokersofmd.com/insurance/uploads/2015/05/Arbitrations-and-Appraisals.pdf

So I think I will schedule inspection and if the estimates come to more than 1k, I will call the Texas hammer guys. Thanks

Can I tell my insurance that I am hiring lawyer to fight with other insurance company?

Oh yes absolutely but after that they LL say give the lawyer information n they won't talk to you

It is your insurance company should be fighting for you . What is your insurance company?

Geico. I would want the lawyer fighting with the other party's insurance.

Contact your insurance company and let them handle. Thats why you pay your insurance and they have experienced lawyer. If you go on your own, you might spend more than worth the damages. IANAL.