Teamplay Rules (most often referred as „Two Headed Giant“) :

There are of course the official rules, which apply to the games: these are the „comprehensive rules“, and in its current form (20. November 2020) 247 pages long. So yes, though they are called comprehensive, they are not that easy to read.

https://magic.wizards.com/en/game-info/gameplay/rules-and-formats/rules

Most of the 2HG rules can be found here in a nicely explained way:

https://mtg.fandom.com/wiki/Two-Headed_Giant

And here is also a Magic Judge blog which answers a lot of questions:

Magic Judge Blog

NOTE that if you google for rules, you might find old rules which are not up to date !!! there was a major rule change with Dominaria. (April 2018)

… Lifegain ?

Rule 810.9: „Damage, loss of life, and gaining life happen to each player individually. The result is applied to the team’s shared life total.“

Let’s say Player A has a Heliod, Sun-Crowned in play, which let’s him put a +1/+1 counter on a creature or enchantment whenever he gains life, and his Teammate B attacks with a Baneslayer Angel with Lifelink, so the team’s Lifepool goes up by five. Nevertheless Player A didn’t gain life individually (the team’s lifepool just has changed). https://blogs.magicjudges.org/2hg/hour-of-devastation-two-headed-giant-release-notes/

You is still just you, even in 2HG. These rules also apply accordingly to loosing life for cards like Vilis, Brooker of Blood – you have to loose life, not your teammate.

rule 810.9a: „If a cost or effect needs to know the value of an individual player’s life total, that cost or effect uses the team’s life total instead.“

Example: In a Two-Headed Giant game, a player on a team that has 17 life is targeted by Beacon of Immortality, which reads, in part, “Double target player’s life total.” That player gains 17 life, so the team winds up at 34 life.

Example: In a Two-Headed Giant game, a player on a team that has 17 life plays Resolute Archangel. The player’s life total of 17 becomes hos starting life total (40). The player`s and the team’s life total is now 40, although just the player who played the Angel gained 23 life.

… True Believer, Circle of Protection Red, Glacial Chasm – are they worthless in 2HG ?

Yes, you are quite right. At least they aren’t that effective as you were used to: a True Believer gives you shroud, but your teammate can still be targetted. Better go for Imperial Mask. You can still play a COP Red, and prevent YOUR part of the damage from an Earthquake, cutting the damage in half at least.

 Once again, you are attacking the team, so why is Glacial Chasm bad ?

• Attackers are declared as a team and are attacking a specific player or planeswalker. If a player does not specify who a creature is attacking, the default is that their creatures are attacking the opponent directly in front of them.
• If an effect prevents a creature from attacking a player, it does not prevent creatures from attacking their teammate.
• If an effect (such as Bane of Bala Ged) asks for “the defending player” it refers to the player that creature is attacking.
• Blockers are declared as a team, creatures either defending player controls can block any attacker.
• Combat damage is dealt to the player that creature is attacking. If an effect prevents combat damage dealt to a player, it does not prevent damage being dealt to their teammate.

The Chasm isn’t a bad card – but it works different than you expect it. If a player has a Glacial Chasm out, he wouldn’t receive damage, but in 2HG the opposing team can circumvent this by simply attacking the other player. Nevertheless, there are cards out there like Territorial Hellkite or cards with Myriad and Encore, which would affect both players of a team, so you can protect yourself.

rule 810.9g: If an effect says that a player can’t gain life, no player on that player’s team can gain life.
rule 810.9h: If an effect says that a player can’t lose life, no player on that player’s team can lose life or pay any amount of life other than 0.

What is the difference to the glacial chasm ?

The damage can’t be circumvented. While the glacial chasm will prevent damage dealt to you only, you should carefully watch out for the phrase „… your life total …“ : if your life total can’t change, damage dealt to your teammate also can’t change your life total. Have a look at Angel of Grace, which has an orcale rules clarification just for 2HG :

„In a Two-Headed Giant game, after resolving Angel of Grace’s triggered ability, damage dealt to you and/or your teammate that would reduce your team’s life total to less than 1 reduces it to 1 instead.“

So cards like Teferi’s protection, Platinum Emperion and thelike do work in 2HG !

 You said that the turns are shared ?

• If a trigger says “at the beginning of phase/step on your turn” (such as God-Pharaoh’s Gift) there is only one of that step each turn so it will trigger once.
• If a trigger says “each player’s phase/step” (such as Howling Mine) or “each opponent’s phase/step” (such as Luminarch Ascension it will trigger once for each player in that step, so twice in 2HG.
• If a player would skip or get an extra step, phase, or turn, that player’s team skips or gets one instead. (rule 805.8.: If an effect gives a player an extra turn or adds a phase or step to that player’s turn, that player’s team takes the extra turn, phase, or step. If an effect causes a player to skip a step, phase, or turn, that player’s team does so. If a single effect causes more than one player on the same team to add or skip the same step, phase, or turn, that team adds or skips only that step, phase, or turn. If an effect causes a player to control another player, the first player controls the affected player’s team.)

This is the reason we banned all „take extra Turns“ cards, or cards which take over another player’s turn (= take over the whole enemies teams turn) – as they are way out of scale, when both teammates get an extra turn. And same goes for cards like Luminarch Ascension or Time Stop. We know there are still some cards out, which aren’t banned (yet), which abuse this mechanisms, but we consider them as not that harmful on gameplay to need a banning.

And yes, we know that a lot of cool cards get banned by the „no extra turns“ rules – and we know lots of you ask for exceptions and say „my planeswalker never triggered ultimate and I will never ever take extra turns…“ but here we do not dissent from our rules : no exceptions, sorry, extra turns for a team are too strong, even if they are not likely to happen.

But what about the other „skip phase“ cards like Stonehorn Dignitary or Recycle ? They became a lot more powerful or about unplayable (your teammate also skips his drawphase, and will get mad if you play such cards..), but we still think they are not overpowered. The strongest card might be Sphinx of the Second Sun, but the card works different than most players think: „At the beginning of your postcombat main phase, you get an additional beginning phase after this phase.“ So basically, you have:

• [ Untap, Upkeep, Draw Step ]= beginning phase.
• First main Phase.
  
• Combat Phase.
• Trigger of the Sphinx. Second Main Phase, -> after this phase
  
• [additional Untap, Upkeep, Draw Step for your team ] *** NOTICE, YOU DON’T GET ANOTHER MAIN PHASE; so you can just use the untapped lands for instants and acitvated abilities. ***
  
• End Step.

Yes, this card will be watched and it is a strong card as additional phases are applied to the whole team. We haven’t banned it yet, though, and we are thankfull for your feedback as always.