This question is essentially the same as my question linked in Radovan's answer. However I will answer your specific questions:
I want that life to evolve slowly and be quite complex, and being structured enough to become intelligent.
It seems that hydrogenic photosynthesis which converts methane and sunlight into hydrogen and biomass is 4-5X as efficient at building biomass as oxygenic photosynthesis but the energy gains from reducing carbohydrates with hydrogen as opposed to oxidising them (the opposite of 'reduction') is 4-5x less.
In my setting, I wish to avoid this effect. However if you are after a slower pace of life then stick with this constraint and simply have your animals need to consume 4-5x the biomass for a terran equivalent energy level or make them have much slower paced metabolisms and lives.
It should not follow very strictly the natural selection (I mean, no one has to have special advantages to survive to predators or something so) and be very different to earth-like life.
Dispensing with natural selection is entirely a separate question to your hydrogen based atmosphere. However, the difficulty your animals have in acquiring energy rich biomass will likely produce very different evolutionary outcomes to that we have seen on earth. Maybe you just want a different evolutionary outcome and pressures? In which case the difference should be sufficient without disposing of natural selection.
The planet has 3 moons and orbits an orange dwarf 5 Gy old, with a luminosity of 0.38 solar luminosities, from a distance of about 1.6 AU.
The hydrogenic photsynthesis process is 4-5 more efficient making biomass than the terran version, so at 0.4 level of insolation you could still end up with twice the amount of biomass we have on earth - but there may be few complex animals. However just because animal diversity might be lower and have slower metabolisms doesn't mean they can't develop complex intelligence - you just need to posit suitable evolutionary pressures to create such intelligence - and overcoming a lack of energy rich food sources as an excellent candidate.
What kind of biochemistry could it be made of? How could it look like? What kind of ecosphere could it develop?
As mentioned in my linked question, a suitable biochemistry for a hydrogen atmosphere is discussed in this paper by Bains et al. He suggests dimethylsulfonium propionate as an alternative to carbohydrate based energy metabolisms but doesn't elaborate on it much further. Please also see my newly filed question Pharbohydrates vs Carbohydrates which has asked exactly this specific question.