If there is exactly 10 card in trash, and I conquer with Last Rites, what cost do I pay for Rhasa? 1energy and power or only 1 power?

You pay 1 Energy + 1 Chaos Power — Rhasa does not count itself toward its own discount.

Trash count is checked at cost-determination (step 3), but step 1 already moved Rhasa from your trash onto the Chain (Rule 354). So with 10 cards in trash, only the 9 that remain count: 10 Energy − 9 = 1 Energy, plus the 1 Chaos Power that no cost reduction touches. FAQ #8430 (and the Last Rites + Rhasa sequence) confirms the played card never counts itself for zone-based discounts.

If by "10 cards" you mean 10 other cards plus Rhasa, then yes — the discount is 10 and you'd pay only the 1 Chaos Power.