-It shouldn't be possible to loose the tutorial repeatedly due to a lucky shot by the enemy before you get control over your units.
You might want to speed up that cutscene and press "Continue" before it does so, then. Never happened to me, though. Also, your initial 2 units automatically take cover behind a nearby destroyed vehicle, so I've no idea how that happened to you.
-Sight lines mean nothing, the halftrack is telepathic.
Lies. Armour is blind outside the front and wherever the turret is pointing as long as the commander doesn't open the hatch and look. I just replayed it to double-check, it really won't notice if you flank it properly.
-A tank with an instagibbing machinegun is not a suitable opponent for the first part of the tutorial.
Did you run right at it or something? It shouldn't even be able to notice you if you run along the left and throw an AT nade at its right side.
-I should not have to waste more then half an hour to figure out how to get past my first tutorial opponent only to be mowed down by apparently unavoidable machineguns 10 seconds later.
You might want to try flanking. Red Army charges don't work with 8 people. And "apparently unavoidable"? There's a gigantic hole in its right flank, there's no one guarding it and you can chuck a grenade at them from behind a house without even being noticed.
In short: Tutorial sucks, does not encourage me to play rest of game.
Perhaps for the better. It only gets harder. I suggest trying Faces of War. It's considerably easier (you control only a squad of infantry and they have pretty high health compared to everyone else) while using more or less the same engine.
Overall, 1C maintains status qou as only publishing good ideas with bad execution.
I fondly think of them as publishers of games which don't hold your hand.