Some cryptocurrencies offer a feature for instant confirmations of transactions. What is required for these instant transactions to take place, how do they happen, and what is required for them to be implemented in Monero (if possible)?
Daughter chains are one of the development goals for Monero. One of these daughter chains could theoretically be used to allow for instant/micro/etc transactions. The idea would be to allow super-fast transactions (or whatever other feature) on the daughter chain, and then settle back to main-chain once a day (or some other interval).
Pretty much any layer 2 system, such as Lightning Network. Doing this on main chain is mostly a bad idea, as mainchain needs to be as secure as possible. Instant transactions have less security (or require some sort of "escrow" to prevent them from being exploited) and so they have to reside on top of the safe-as-houses mainchain.