Few questions

1. Are Vickers LMG (much) better than Brens, and is it worth going for them?
2. Which commanders should i choose from: Royal Artillery, Royal Engineers, Commandos, Special Weapons and Advanced Emplacments?
3. When should i choose which doctrine and how to use it?
4. How to counter indirect fire and support weapons spam as Brits?

1. They should have identical statistics. Generally getting a Special Weapons Halftrack would be great if you want to keep up field presence. It's very good for reinforcing in the field and upgrading in the field. The Halftrack and its weapon drops have definitely lost some of its attractiveness due to no longer bypassing tech.

2. Special Weapons is the safe choice right now, as it is the only commander with access to AT snares. Additionally, it is quite powerful in the late game as well, with concentrated arty and the Crocodile. Commandos are very strong close-range units, and the rest of the abilities in the commander are nice too, but eats a lot of munitions. Royal Engineers is good for the flamethrower (very important on urban maps), Command Vehicle is strong, flame mortars are decent, and the AVRE in late game is great for wiping vetted infantry and team weapons.

3. You can choose it reactively or purposefully. For example, if your opponent is going nuts on light vehicles, choosing Special Weapons for the Tank Hunter Infantry Sections would be a good idea. If your opponent is spamming machine guns and other team weapons, you might want to try Commandos for the Smoke Raid and then drop Commandos in behind them. These are reactive commander picks. If you find yourself in the late game with a decent army and want to close the game out, you might want to pick Royal Engineers for the AVRE, which wipes squads quite effectively, making it hard for your opponent to use infantry.

4. Indirect Fire is tough because Brits have odd indirect fire options. If there is only one mortar, you can consider building a Mortar Pit to bomb the crap out of it. However, if your opponent has gone for leFH 18s, don't build emplacements because they get hard countered by howitzers. Instead, you must rely on smoke (blocks line-of-sight) and an attack with infantry, preferably supported by tanks. Commando doctrine is generally well-suited to countering mass support weapon play. Alternatively, you can buy the Mobile Assault Doctrine and get a Land Mattress.

Thank you for answering. I have few more questions:
1. Is there vehicle that is the best option for vehicle commander? Is AEC worth for make it commander?
2. When to choose Anvil and when Hammer specialization? Is Hammer even worth taking?
3. Are they units that are not worth taking?
4. When should i get upgrades for granades, weapons and additional squad member?

1. I'm sorry, could you clarify "vehicle commander"? AEC is usually a stopgap option if you need to counter a Luchs, 222, or 251.

2. Anvil or Hammer depends on your build and your opponent's build. Anvil is strong for the Churchills--excellent for soaking up fire from enemy AT, especially Panthers. Heavy Sappers are great for increased repair speed. Hammer is strong for the Gammon Bomb--makes your IS deadly against garrisons and able to wipe squads if your opponent is inattentive. Comets are strong against P4 spam.

3. Everything in the Brit roster works. Even the Bofors, which you can plop down very late in the game as a surprise to lock down a VP. But in most cases, Emplacements are the units that you need to think twice about using because they are easily hard-countered.

4. Usually Bolster Squad first, weapon upgrades second, before you get your company command post. Grenades I find useful in the late game when both of you are tired and you are more likely to catch your opponent not paying attention to his squad. However, this is all my own playstyle, and other playstyles work.

By commander vehicle i mean command vehicle - ability from Royal Engineers Commander. I don't know why i remember name of this skill like this. Tnaks again for answering.

The Command Vehicle applies a nerf to the command vehicle itself, thus usually players build an AEC in mid game to help against light vehicles, and once medium/heavy armor arrives they upgrade it into a Command Vehicle. This way the lose less combat power because the AEC becomes somewhat obsolete as the game progresses into late game.

Alternatively, you can designate the Churchill AVRE as a Command Vehicle, as it does not suffer much from becoming a Command Vehicle.