Great advice.
And the poor Shih Tzu, it is very clear to see the wounds are clipper cuts from the end of the clipper teeth being jabbed into the skin. Did the owner take him back to the groomer to show them what they had done (that deserves at least a refund!!), or perhaps just take them the pictures, i wouldn't want to make him go back to a place where he has such a nasty experience.
I hope his wounds recover quickly and your friends send him more regularly to a good groomer who will give him the respect and good grooming experience he deserves.

Your dog is probably a little car sick, you can get them out of it. Start by getting her to sit in the car with the engine off. Stay with her for a few minutes, give her a few treats and tell her she is good (but don't make a huge fuss or go over the top, let her know that being in the car is a very normal thing), do this a couple of times a day for 3 days). Next turn on the engine and put her in the car, repeat the treat giving and stuff, again for 3 days. Then get in the car with her (engine on) and take a short drive (like up and down your road, or around the block, less than 5 minutes is enough to start with), do this every day once or twice for a week. Slowly start to increase the distance you travel with her in the car and usually most dogs will overcome the car sickness.
Make sure you don't go for a drive with her for at least 2 hours after he eats (as the food can cause her to have more pronounced sickness).

As far as the mats and dandruff goes. If you think a Shampoo is causing skin problems (like the puppy shampoo causing dandruff) try just changing shampoo to a very natural and most importantly fragrance free shampoo before going for something medicated. The sulfur shampoo will dry out the coat and cause the coat to mat faster than it otherwise would (but more about mats later). It is best to try and avoid medicated washes as much as possible for minor problems (such as dandruff) as the skin can build an immunity to them meaning if a more serious problem comes along you need to use a more serious medicated wash.

As far as ticks go. Frontline spray won't be 100% effective unless you get it all over the body (making it quite tricky to use) a better option is to go for one of the spot-on products (Frontline-combo or Advantix). Alternatively you can choose to use Revolution (which prevents ticks, fleas, mites and heartworms).

On to mats. There are only 2 ways to stop mats: Brush your dog regularly or keep the coat very short. Although there are many things that can make mats appear faster (coat condition, coat length, activity level etc.), daily brushing will keep them away no matter what.
If you see/feel mats in your dogs coat, brush them out before bathing, bathing will only tighten the mats and make them harder to remove. If you leave them in longer, eventually they will be impossible to remove (not to mention painful for your dog) and need to be shaved/cut off.