PoS issuance rewards are 4.6%/year, which can be offset with burn rate, but it is at 0.5% now.

The site projects that in 200 years, burn and issuance will be at equilibrium.

PoS issuance is 4.6%/year per staked ETH.

Only 14M of the total 120M ETH are staked right now, making the real issuance only 0.5%/year when taken as a percentage of total ETH supply.

Subtract the 0.5% burn rate from that 0.5% real issuance rate (with rounding errors), and that's how you get Ethereum's current situation of being "pretty close" to deflationary.

Will gas fees burn or go to stakers?

EIP-1559 is the Ethereum patch that introduced the fee burn in Aug 2021.

It's a bit complex, but basically speaking, the higher demand is for the network, the more expensive transactions become and the more ETH gets burned.