दाती तृण धरणे

Yes, but mostly in writing, news, and formal speeches. It's rare in casual texting.

Only if you've made a catastrophic mistake and want to be very dramatic/humble. Otherwise, it's too much.

'गवत' is the common word for grass. 'तृण' is the formal/Sanskrit word used specifically in this idiom.

No, it's a sign of extreme humility, though it does imply a position of weakness.

It's culturally rooted in Hindu values regarding cows, but the idiom itself is used by everyone regardless of religion.

In the past tense, it remains 'धरले' because it agrees with the neuter object 'तृण'. Example: 'तिने दाती तृण धरले'.

People sometimes just say 'शरण आला' (he surrendered), but it loses the 'grass' imagery.

Yes, friends might use it sarcastically when someone finally admits they were wrong about a small thing.

'दंड थोपटणे' (to challenge/fight) or 'शड्डू ठोकणे'.

Yes, similar concepts exist in Hindi (दाँतों तले उँगली दबाना is different, but 'तृण धरना' exists in old literature).

Because grass is the food of the cow, the ultimate symbol of a non-combatant in ancient India.

Yes, to describe a team that gave up completely without a fight.

No, it's an old locative form. In modern Marathi, we usually say 'दातात'.

It's B1/B2 because it requires understanding of figurative language and cultural history.