If you have multiple desired essences, their probabilities add up because each roll can only match one target at a time, these are mutually exclusive outcomes.
Per-Run Probability
Each run gives you multiple essences. The chance of getting at least one match:
P_run = 1 − (1 − P_essence)^essences_per_run
Confidence Levels
How many runs to reach X% confidence of getting at least one match:
Runs = ⌈ln(1 − confidence) / ln(1 − P_run)⌉
Sanity Regen
1 sanity regenerates every 7 minutes and 12 seconds