I totally forgot its title, but here are things which I remember:

1.It's game with space ships, with control in manner relatively similar to games like Asteroids.
2.However in this game camera is following our ship and we're playing on the "closed" area.
3.It had multiplayer option on the same computer (I think then it was working as split screen), players were basically fighting with each other.
4.Game was probably published on 1999 or 2000, for sure it couldn't be later than May 2000 (it was present in some magazine published on May/June 2000).

Incoming comes to my mind. There's also a sequel called Incoming Forces.

Both games are available on GOG:
https://www.gog.com/game/incoming_incoming_forces

For 100% it's 2D. I'm not sure about sound effects though. It's definitelly not Incoming - it was freeware, 2D and with view of the ship in the similar style like in Asteroids or Galaga (so from outside the ship).

Operation: Inner Space? [url=https://en.wikipedia.org/wiki/Operation:_Inner_Space]https://en.wikipedia.org/wiki/Operation:_Inner_Space[/url]

Not sure if it was freeware (probably a fairly large shareware game), but I remember getting a copy on a coverdisk.

Transcendence?

https://transcendence.kronosaur.com/

Was it top down view?
Think then I know what you mean but my damn memory sucks.
Shots bouncing off the screen etc.?
And you had some kind of thruster and need to carefully maneuver through obstacles too?

edit: finally remembered the name: Subspace :-D

Unfortunately not, I remember that this game didn't had any "merchant" aspect. Unfortunately not, I think I remember that vehicle sprites were bigger and there was more "terrain" on the level. But I feel we're getting closer. Yes, top down view! Quite probable that shots bounced off the screen, I'm almost certain that there was present the aspect of "thrusters".

Disclaimer - I know about the game "Head On" from 2001 and Gravity Force from 2000, but sadly these are not the game I'm looking for.

I bought that game actually, was a 1994 game windows 3.1. But it wasn't multi-player, instead you had a faction you were part of and some would challenge you to duels (the only 'legit' way to kill and a great way to get resources). The shareware gave you almost the whole game, one or two things were missing, the disk included a ship editor to add your own ship designs to the game.

Though if you wanted to play that again, you could almost go with RingRunner, as a similar feel and racing tracks unlocked later; though i'd say RingRunner is better designed there's nothing quite like flying a dolphin in space belching fireballs...

Inner space wiki link

The Ur-Quan Masters (an open source remake of Star Control II)? Although the single player campaign is the main mode, there is a melee mode for two players.

edit: Forget it, now I saw that the remake was released in 2002.

Star Miner by Positech sounds similar, but that had a mining aspect you'd probably remember and I'm not sure about multiplayer.

https://www.youtube.com/watch?v=v1fseBg0E-g&ab_channel=Valthero

Just checked it, but sadly it's not that game either - sprites of ships were bigger in game I'm looking for and there was same screen/PC multiplayer.

Maybe one of these?: https://www.mobygames.com/game-group/asteroids-variants/offset,25/so,1d/

Unfortunately none of them, I've already checked in MobyGames.

Given the description and that you already checked Mobygames, I'll just presume it isn't Gravity Well or Critical Mass.