If I use Sacrifice to kill my mighty unit and I have Altar of Memories in play and readied, what is the order of operations of triggers and resolution? Can I draw with Sacrifice before doing Altar trigger?

Yes, you will draw for Sacrifice before the Altar of Memories trigger is put on the chain.

According to the rules and the RiftJudge FAQ for Altar of Memories (RiftJudge FAQ #7577), triggered abilities do not resolve immediately upon the inciting event; they are added to the chain as "pending" items and finalize during the next cleanup after the current action finishes resolving.

Sequence of Events:

1. Playing the Spell: You announce Sacrifice and choose your Mighty unit as the target for the "kill" cost.
2. Paying Costs: You kill your Mighty unit. This satisfies the cost for Sacrifice.
3. Triggering Altar: Because a friendly unit died, the Altar of Memories trigger condition is met. It is added to the chain as a Pending Item.
4. Resolution of Sacrifice: Sacrifice finishes its resolution: you draw 2 cards and channel 1 rune.
5. Finalization: With Sacrifice fully resolved, the game moves to the "Finalize" step (Rule 340.3). The pending Altar of Memories trigger finalizes and is placed on the chain as a chain item.
6. Resolution of Altar: You now have priority to resolve the Altar of Memories trigger, allowing you to exhaust it to draw 1 and manipulate your deck.

Summary: You get the cards from Sacrifice first. The Altar of Memories ability only enters the chain once Sacrifice has completely finished resolving.