1) Does army sometimes attack an ennemy position with only 1 fireteam? Or is the squad the smallest unit attacking an ennemy position?.
Well, the smallest unit to attack an enemy position would be a single rifleman! It's like asking "how long is a piece of string?" It entirely depends on the situation. But doctrinally the basic rule is "Three is to One" - ie the attacker must have at least three times the men of the defender. So if the enemy position consisted of two men, you'd generally want more than a single fire team. But like I said, it depends on the situation. If those two men had a GPMG and were well dug-in, you'd definitely want more than a squad to launch an attack.
2) In British Army, why do both fireteams forming an infantry section have 1 LMG (Light Machine Gun)?
So that both fire teams have a suppression weapon.
What does the private carrying the LMG do in the fireteam chosen for maneuver during a squad attack?
He assaults with the rest of them, and trust me, it's not fun being that private when you're leopard-crawling with the damn thing!
Isn't the LMG a weapon for suppressive fire?
Yes, but there's no reason he can't use it for suppressive fire during the assault as part of the maneouvre team. It won't be the most accurate shooting but he'll still get a lot more rounds downrange than the riflemen in the team.
Wouldn't it be better to have LMG for only 1 fireteam which would be always chosen for base of fire?
You can't always choose which of your teams is going to be the base of fire. Particularly in complex terrain, and in things like counter-ambush drills. It's better to have both teams capable of doing both roles.
What's happened is that LMGs have gotten lighter but they pack less firepower (say, the Minimi compared to the M-60). In the Cold War days there was a big imbalance - your assault team was all riflemen and consisted of the bulk of the squad, while your suppressing team had a MMG and was only a few men. This was necessary because it wasn't really possible to assault with a MMG, particularly if it's a two-man team. But this isn't the best situation in complex terrain like MOUT because you only have one team capable of operating properly. The three-man MMG team isn't much good for clearing rooms, and so on.
These days things are trending towards two equal fireteams because the LMGs are lighter. This means you can assault with them (kind of!) but two automatic weapons per section are desireable so you can use either team for either task, and also because LMGs like the Minimi don't offer as much firepower. So now either team can assault and either team can be fire support. You can also fit more teams together if you need to - you might use three teams for a particular task, and you can use them all interchangably without worrying whether you've ended up with three rifle teams, or three machine gun teams.
This is why modern fire teams are sometimes called "bricks" - because they are the "building blocks" that you can build bigger forces from.
