No, you won't get priority during a spell's or ability's resolution. If the effect instructs you to 'repeat this process', then you have to repeat the process for as long as you can.
Instructions of effects are always mandatory, unless the effect itself offers you a choice. "If you win, repeat this process" does not involve a choice. You keep clashing, losing life, and drawing cards, until you fail to win a clash. There are cards that allow you to either continue or stop a process, but they include "may" somewhere in their wording, as do all cards when taking an action is voluntary.
- Resolving Spells and Abilities
608.2c The controller of the spell or ability follows its instructions in the order written. [..]
The active player gets priority only after the current spell or ability has finished resolving:
117.3b The active player receives priority after a spell or ability (other than a mana ability) resolves.
Each instance of "lose 2 life" is separate. If there is an ability in your game that triggers on you losing life, it will trigger each time you lose 2 life during Hoarder's Greed. Since you can lose life regardless of your current life total, as opposed to "paying 2 life" which you can only do if you do have 2 or more life, the lower limit to your resulting health depends only on the number of repetitions of the process, and thus on the number of cards in your library.
119.3. If an effect causes a player to gain life or lose life, that player’s life total is adjusted accordingly.
119.4. If a cost or effect allows a player to pay an amount of life greater than 0, the player may do so only if their life total is greater than or equal to the amount of the payment.
The process stops only when you fail to win a clash, i.e. you reveal a card with lower or equal CMC, or when you can't reveal a card at all because your library is empty.
701.22d A player wins a clash if that player revealed a card with a higher converted mana cost than all other cards revealed in that clash.
Note that you don't lose the game during the resolution of a spell, since state-based actions are not being checked at that time.
704.4. Unlike triggered abilities, state-based actions pay no attention to what happens during the resolution of a spell or ability.
If, in the process of resolving Hoarder's Greed, you go to 0 life or less, or try to draw from an empty library, you will lose as soon as the spell has resolved and the active player would gain priority, because at that time, state-based actions are checked.
704.3. Whenever a player would get priority (see rule 117, “Timing and Priority”), the game checks for any of the listed conditions for state-based actions, then performs all applicable state-based actions simultaneously as a single event.
