Question 1&2, they are actually linked as switching to hydraulics (1) will require to change the brifters, which will make the switch to (2) not so expensive (if you consider the price of 12-speed related to the mandatory change to 11-speed to have hydraulic): the gravel market is what it now, and you got a groupset with an excellent price quality/ratio, if not the best ratio. In the current state of the market, I don't think it's worth upgrading it, unless you are ready to spend the price of the bike. The groupset is not perfect for sure, but you need to go very high in the range to get one that is better in every way.
Gravel groupsets are kind of a paradox to me, gravel bikes are sold as versatile bikes, but this is not reflected in the range of the transmission. Currently, most hydraulic gravel groupsets (all Shimano single chainring, SRAM Apex) have in common a 11-speed 11/42 cassette (you have 10-speed 11/48). Which means a lower range than what you have now: you'll have more "intermediate speeds" to optimise your cadence — which is a must for performance oriented road bikes, but it will be harder uphill. To have more range, you'll need either to upgrade to the most expensive 1x ranges (Campagnolo Ekar, SRAM EXPLR) or Shimano 2x (that also have narrow ranges for 2x transmissions, if your bike allows it, which is not certain from the pictures). The first option will cost about 1300€ (in parts), the second option between 700€ and 1000€ (the price of the Topstone 4 is 1500€ here, for comparison). So quite an expensive operation, for something that could come with a regression, if you value range.
So put it simply, you have a good bike now, enjoy it, and upgrade when components are getting worn. And this point in time, hopefully you'll get better transmissions that the ones available on the market now. The turning point will probably be when Shimano will upgrade their gravel transmissions (that are for future reference GRX400/600/800). As long as they don't do it, the others won't have any incentive to improve their offerings at lower price points.
For question (3), going to a shop to a simple maintenance is advisable — most shop actually offer a first check for free, as it is known that some screw got loose on new bike. Ask them at the same time to adjust the brakes, maybe they are not adjusted properly.
Unrelated to your questions, two opinions:
- the best understated upgrades you can do are a carbon seatpost (that will improve your comfort significantly), and going tubeless — your bike already has quality tires, so no need to upgrade them.
- if you consider going slick - your question (4), you'll compromise the ability of the bike to go offroad, which is the point of gravel bikes. Changing tires is not an expensive operation, and reversible, so you shouldn't hesitate doing it. And if you realise that you don't miss the offroad abilities, selling your gravel and buying a road bike will probably be a better operation than upgrading a gravel so that it "doesn't suck" as road bike.