I have heard many good things about this one, but I'm completely stuck on the first levels.
The missions are too damn hard and the controls are a pain in the rectum.

If I try to sneak up on someone with the fibre wire, they just turn around and shoot me. Even when I'm crouched.
If I shoot someone, some idiotic pedestrian will see it (even when I double-check to see if anyone sees me!) and guess what, "the meeting has been cancelled"...

Is this game some sort of bad joke? Is it designed to torment people?

I guess this game is from the generation of gamers, who doesn't mind failing about 34349 times before finally figuring it out...

It's been some time since I played it but I don't remember Hitman 1 being any harder than other games in the series. Mission 7 in Hitman 2 was more frustrating than the whole of Hitman 1.

I dunno, I find the first game less frustrating than Hitman 2. The sequel was just as frustratingly difficult as the first one but it also had the elusive Silent Assassin rank to taunt me whenever I didn't achieve it. In the original I had no problem sniping and killing anyone in my way, sneaking 90% of the level and shooting my way during the last 10% if it made my life easier and improved my survival chances, something I couldn't do in Hitman 2 to ease the unfairness or the ultra paranoid AI in some levels, lest I wanted to kiss good bye that damn Silent Assassin rank.

Hitman levels where things change with time can be annoying, like the Triad meeting level you mention. I enjoyed both stealth and combat approaches to completing levels, so if you get stuck on stealth, consider picking a fight someplace else to see what happens. On to specific points that might help you:

-- "sneaking ... fibre wire" --
You move slowly, and anyone seeing you with piano wire knows you're an assassin. The knife is silent, and faster. I ready the knife without drawing it, then walk so close behind someone I'm bumping them - not sneaking, but walking. And then I draw and attack with the knife in as quick a motion as I can click.

-- "idiodic pedestrian will see [me shoot someone]" --
That was pretty frustrating on that level. There's a guy who always comes around the corner. I had to wait for the pedestrian to turn a corner - almost letting my target reach the main street, and then acting. Also, drop your victim down a sewer hole or someplace out of sight, or the alarm will be raised later. The game isn't always this harsh.

-- "doesn't mind failing about 34349 times" --
Don't get too caught up on the one guy. Try going to the restaurant meeting location and looking around. One of my favorite combat approaches to this level was to wait for the two people meeting to sit down in plain view of the street. Several bullets and a broken window later, the targets were dead (but if the messenger is still around, he'll probably run to escape).