hey, why not try out fish4dogs? get the one for puppy. i got the one for adult as bailey's 6 year-old now. it's been almost a week now and i thought it works super with her. she loves the kibbles, i feed it to her twice a day, morning and night, about 3/4 cups each time. small differences i realised from fish4dogs from the other kibbles is that
(1) she now isnt hungry all the time (even though i have not changed her feeding amount)
(2) her poo looks healthy (in my own opinion) and she poos once daily. on other brand, she sometimes skip her poo session by a day!
(3) her poo doesnt stink so badly

the brand she's tried (in order) natural balance > artemis > canidae > addiction > fish4dogs

give the brand a try and if your dog doesnt like it at all, you can exchange it for another brand (at pet safari).

Sometimes skin issues cannot be fully controlled with diet alone (although a good diet will go a long way to controlling skin issues). Schnauzers (especially ones that aren't bred so carefully) are especially prone to a number of skin issues and are notorious for sensitive skin and allergies.
The food may not be 100% effective because there is still an underlying issue that needs to be resolved (fungus, environmental allergy, hot spots etc). Also it sometimes takes a long time (up to 6months in some cases) for the negative impacts of a not so great food to fully filter out of the system (and so stop affecting the body). It could just be that the initial change in food gave the skin a boost, but the lingering dry skin is just caused by the old food still working its way out of the system.

Some useful things to know to better assess the system include:
What shampoo you use and how often you bath him.
How long you have been feeding the new food.
What the dry skin looks like (is it flaky, red, oily, itchy, broken skin, bumpy).
Where the dogs stays (is it dusty, type of flooring, what the floor is cleaned with, possible access to other animals).
When the dry skin started (and if anything changed at that time, when you brought him home, changed bed, changed shampoo anything new that could cause stress or allergies).

You can try changing food again, but if you found something that made an obvious improvement i would stick with it for at least 4 months to see if there is more improvement to come before switching again.

Ok in order:
Pet Esthe should be fine. Consider changing if nothing else works just as a test, but i would highly doubt it would cause the problems.
Once per week is fine. Make sure you dry him off really well (you can use a hairdryer but make sure the hot wind doesn't blow too close to the skin as it can burn/irritate.
I would definitely stick with the same food for another 2 months to see if the skin heals fully. If you want to switch after that, you can but at least you know 1 brand which fully clears up his skin in case the problem comes back.
The small red spots sound like hot spots (are they quite spread out like bug bites or more clumped together like a rash?), and the dry flaky skin could just be dandruff or where the skin is healing. Sounds like quite a minor thing at the moment but still best to get it fully cleared up.
The area sounds fine, if you use strong chemical floor cleaners/detergent to clean his bed it could be causing him some irritation but you would most likely see localized irritation from that, usually on the belly, feet and underside of the legs, with very little or none on the back and head (basically only on areas that come in a lot of contact with whatever is causing the irritation).

Random question: why would you buy a puppy who already has skin problems? it is something i come across quite often (well more often that i ever expected when i started out in the pet world), people who would never (for example) buy a car leaky gas tank or a washing machine that only works on one of its settings will happily shell out money for a dog with health issues...

Using the Frontline every week could definitely be adding to the problem. Fontline used very often can irritate and dry out the skin which could be keeping the initial skin problem from fully healing. It is usually only necessary to use once a month (make sure you apply it at least 2 days after AND before bathing). If you find that ticks are still sticking to your dog, try using one of the Spot-on products (Frontline-combo, Advantix, Revolution) for a while (they are easier to apply than the spray) to see if the skin clears up fully (again once a month is usually enough and make sure it is at least 2 days after a bath and 2days before the next one.

As far as amount of food is concerned. Every dog is slightly different. A page or so back (on this thread) is a chart/diagram showing the ideal 'look' for a dog (not too thin and not too fat), in line with that, i always say if you can feel the individual rib bones easily and see the pelvic/hip bones (sticking out above the hips) the dog should eat more, if you can't feel the ribs and your dog has no 'tuck up' (where the body slopes upwards towards the back legs) and has a belly hanging down or a stomach that constantly feels hard and bloated the dog should eat less (or be dewormed or checked for cushings disease). A dog that is the right weight will look heathy, you can feel their ribs but also feel that there is a layer of fat between the ribs and the skin. A healthy (and well fed dog) will have bright/shiny eyes (but not glazed which is a sign of illness) and pink gums.
You can also use your dog's reaction to food as a sign of how much to feed them (although some dogs will act starving no matter how much you give and others will appear disinterested/ full no matter how little they eat). In general, if your dog still begs for more and licks the bowl clean, he might do well with a little more food, if he leaves a few pieces in the bowl or plays with his food towards the end of his meal he could eat less.
What you are feeding sounds about right for your dog, but it can vary greatly from his size (as with a lot of breeds here some dogs are very small and some are very over-sized) and activity level.