Some very interesting questions.
I`m a beginner to CIV series, and I have read these forums for almost a month now, and I`ve noticed that the thing that I almost always fail is city placement. My priorities are always resources. The more I can get in my fat cross, the better. I might even deny myself a fresh water bonus or coastal for additional 1 resource. I consider them as improved improvements, and I`ve never really considered a fresh water bonus "that" great, after all, there are other ways how to improve city health, right? So I`d kinda want your advice here - what are the priorities for city settling, and why?
You are right to consider gaining control of resources as important. But remember a resource need only be inside your cultural borders to be of use as a resource. Once your city gets 100 culture it will expand its borders to 1 tile outside the fat cross, so sometimes it is better to wait 20 or even 50 turns for a resource you don't need immediately rather than mess up a city's placement for the rest of the game. So one tactic is to position the city ideally and then build a couple of buildings that will expand your culture quickly.
Also consider using two cities to get all the resources in a region rather than trying to do the impossible with one city, one big powerful city placed ideally and a little helper city that gathers a few more resources but will never be fully developed itself. Not all cities need to grow to work 20 tiles or build every building, it helps to have a mixture of sizes and roles. I find overlapping the fat crosses of two cities especially worthwhile if the cottages of the big city can be worked by the smaller one while the big one builds its infrastructure (whipping or working mines). Later on the small companion city makes a great drafting city and can be used for spamming missionaries or catapults. In BtS a small city can be very useful in the late game by building all the espionage buildings.
The fresh water bonus is very important for a city. It is worth 2

and that is the same as the aquaduct gives a city, so in that sense it's worth 100 hammers, although I'd put it higher as you can build the aquaduct as well (a case of having your cake and eating it

). In BtS a riverside tile is even more important if there are a lot of river tiles in the city's fat cross as each one gets the +1 hammer from the levee building. That frequently influences my city placement in 4000 BC even though the levee might not be built until 1600 AD
Also, I`d like to start specializing my cities better than I`ve done it before, so my second question is - if a certain spot could be, let`s say, a bit more favourable for a GP farm than a production city, but I already have a GP farm, and I really lack production cities, and sadly there aren`t better spots availabe, should I deny myself the more supreme GP farm and build a bit questionable production city, or is it logical to simply cope with the fact that my wonder and troop production will be low, but at least I`ll get more great people? And if I chose to make it a production city, is it usually advised to build production boosting improvements even on grassland riverside tiles, if I have enough food resources nearby?
That is a hard question to answer, it really does depend on the game and map and even the situation at that stage of the game. Making more GPs will not be a replacement for having adequate production. If you want to make war or avoid being attacked you need adequate production.
Fortunately a GP farm can in some ways serve both purposes and sometimes be converted from one to the other. If you run or switch to Slavery then the food a GP farm produces can be converted to hammers, so if you have 2 GP farms and you're attacked, both can be whipped to meet the emergency

You can (and I do) think of your specialists in the GP farm as potential recruits for the army. I often research some key military tech and then whip my specialists into the army to rapidly exploit the technological advantage.
Also if the second city has a lot of farms then you can confidently start out as a GP farm until the cost of producing GPs starts to get high and then convert the farms into workshops. By happy coincidence the efficiency of workshops versus farms increases as the game progresses. With State Property, Caste System the grassland farm (produces 4 food) can be coverted to a workshop giving 2 food and 4 hammers at about the time GPs start to cost a lot of GPPs. This is also the time when units cost a lot of hammers.
So I would say that it is not really a problem for a SE ( or Hybrid) to decide between using a captured city for either hammer production or as a GP farm. You can to a limited extent have it both ways.
Where could I get more information about coastal bonus, and why is it that good?
Thanks. A bit complicated, but I hope you`ll get the idea.
Not sure what you mean by coastal bonus. The only one I know of is the +1 commerce over an ocean tile, but I see that as an ocean nerfing becuase it is too far from land.
I guess you could mean why is it so good to place your city on the coast instead of 1 tile inland. There are several reasons why a coastal city is good and one why it is bad. A coastal city can build several extra buildings that are not available to a landlocked city, lighthouse, harbour and drydock and several wonders GLighthouse and Colossus. Those buildings can give better income and faster growth. Obviously it can also build workboats and ships that a landlocked city couldn't. On certain maps that is a major consideration. The disadvantage is that it can be attacked from the sea in a sneak attack in a way that a landlocked city can't be. So you need to be bit more careful to protect a coastal city and be wary of potential enemies and invasions.