No. 1, the coating shop is wrong because nothing wrong with using "expensive" car wash products (if you have the money to burn). the more accurate advise is to use a good PH neutral car wash shampoo. this is vital because any acidic/alkaline car shampoo while able to give stronger cleaning power but will also wear off / erode any types of LSP much faster in the long run.

No. 2, you can absolutely apply waxes on top of your coating, nothing wrong with that but you'll probably just wasting money because coatings are generally hydrophobic in nature. you'll probably get the wax to stay on the surface for a week or two before it all washes off.

No. 3, tire shines and any other surface protectants for that matter are meant to wear off no matter which brand/type. they are meant to be a sacrificial protective layer. try prepping your tires properly before applying your tire shine, that should allow it to last longer. Soft 99's BLACK.BLACK is a good recommendation, while it loses it shines overtime but the tires remains "matte" and some prefer the latter.

No. 4, as for the interior, unless you expose your car to long hours of sunlight then there's no need to constantly worry about applying surface protectants. just a quick wipe down with a damp cloth after your car wash will be sufficient. most good interior detailing products are water soluble / based nowadays anyway, can't think of anymore that are oil based.

No. 5, for windscreen, you can consider using Soft 99's Glaco - have been using it for my 3 cars and never experience any premature wear and tear on the wiper blades.

(1) there are tonnes of good PH neutral car shampoo from reputable brands out there, you can start by browsing the aisles in ACE Hardware to get an idea - as long as they are PH neutral then you are good. alternatively if you want to be kinder to your wallet then you can consider Osren's Nano wash.

(2) generally, a properly coated car only needs weekly or bi-weekly car wash with a good shampoo for maintenance. no actual need to "top up" or any other "fancy schmancy" stuffs but if you want, i'd suggest getting a spray-on quick wax instead of a quick detailer because detailing sprays are usually aimed to remove contaminants or to clean surfaces in situations where a car wash is not feasible. spray-on quick waxes are usually much more lubricating hence minimizing the chances of introducing scratches or swirl marks.

(3) only use one type of product, if you like how your current tire shine works then stick with it, if not, you can try Soft99's BLACK.BLACK. frankly, i wouldn't trouble myself with tire shines because it will get soiled the very moment i drive it out of the house (no matter how pristine i made it during the car wash).

have fun exploring - the world of car washes / detailing is interesting and mind-boggling all at the same time but most importantly, do what is most convenient for you.

don't. they might scratch your car. Just use the soft99 to be safe..
you're trying to remove the watermarks? try something more acidic like carpro descale?