#holding priority

If you have unlimited mana, you can do this, yes. You’ll just have to hold priority and put all the activations on the stack at the same time. If you activate the ability and let it resolve then activate it again, etc., Xantcha’s controller will lose the game before you’ve drawn your whole deck and Xantcha themself will no longer be in play. 

TL;DR: Yes, just hold priority.

Priority and the Stack

APNAP stands for Active Player, Non-Active Player, and is the order in which almost anything in the game is done if more than one player needs to do it. First the active player (the player whose turn it is) will make his or her decision or perform some action, then each other player in turn order will do the same. The active player is always the first player to receive priority in a given step or phase.

Priority is the system whereby players are allowed to cast spells, activate abilities, and take special actions. Only a player with priority can cast a spell, activate an ability, or take a special action. (With the exception of generating mana via mana abilities when a mana payment is required by that player.)

The Stack is a zone like the battlefield or exile. It’s where we put spells and abilities that are waiting to resolve. Spells and abilities on the stack resolve in a last in, first out (LIFO) order. This means that the newest object on the stack will always be the first to resolve.

Any time a player would receive priority, we first check state-based actions and deal with those, then we put any triggers that have triggered onto the stack. If multiple players have triggers to put on the stack, they’re put on in APNAP order. Once there are no more state-based actions to deal with or triggers to stack, the player finally receives priority.

When a player casts a spell or activates an ability, that player will receive priority again afterwards.

When a player passes priority, the game checks state-based actions and triggers again before priority passes to the next player in turn order. A player must announce any mana in his or her mana pool when her or she passes priority.

When all players pass in succession, the top object on the stack resolves, or the current step or phase ends if the stack was empty.

Players can always add new spells or abilities to the stack if they have priority. At no point do we “resolve the stack” without players being able to respond.

Holding Priority

Holding priority just means that you want to respond to your own spell or activated ability.

It depends on exactly how your friend activated the abilities.

If he activated one Bomat Courier, then held priority and activated the other Bomat Courier, then yes, he would get all four cards into his hand since he’s past the point of needing to pay the cost of the second ability.

If he activated one Bomat Courier, let its ability resolve, then activated the second Bomat Courier, then he would have to discard the cards from the first Courier to activate the second since those cards have already gone into his hand.

You can cast Eerie Interlude either before you cast Cataclysmic Gearhulk or in response to its trigger to get the effect you want here. In either case, the creatures exiled by it won’t be on the battlefield when Cataclysmic Gearhulk’s trigger resolves and will be safe from its wrath.

(Just remember that if you want to respond to your own trigger here, you need to explicitly announce that you’re retaining priority after putting it on the stack. Something like “Gearhulk resolves. Trigger on the stack, I cast Eerie Interlude targeting...” would work just fine.)

Whenever you want to respond to your own spell or activated ability.

When a player casts a spell or activates an ability, that player still has priority once that spell or ability is on the stack. Holding priority means they’re responding to their own spell or ability before it resolves rather than automatically passing to the next player as is much more usual.

You need to announce it in one block of actions so your opponent doesn’t reveal their hand just yet.

Something like “Gitaxian Probe you. Holding priority, Remand it.”