How do naked options work on Robinhood?

From my understanding of Robinhood's options knowledge center, without the ability to exercise the option (i.e. I don't hold 100 shares nor have enough cash to buy 100), I cannot write contracts. Instead, I am only able to buy already written contracts, and I can only sell my contracts back to the market. In fact, Robinhood states that on expiration, the option will be "automatically sold back to the market a few hours before market close".

Small detail but the contract that you buy does not have to be 'already written'. The counter party may be selling to open (STO) when you buy to open (BTO).

In the US, if an option is one cent or more in-the-money (ITM) at expiration, the Option Clearing Corp (OCC) will automatically exercise options whether they are long or short. This is called Exercise by Exception. For equity options, you will end up with a long or short position in the underlying (index options are cash settled).

If you are long the option, you can designate to the OCC via your broker that it is not auto exercised at expiration. This would make sense if it is ITM by pennies and your commission and/or fees to close the position exceeds the ITM amount.

That is why Robinhood closes options a few hours before expiration. I think that it's an unfair practice if there's no notification because it can lead to undue investor risk - but that's another story.

My understanding of such a sell transaction is that it would require 3 parties: myself, who owns the option; someone interested in purchasing a covered call; and someone interested in purchasing a covered put. This is the only way I imagine I can sell the option without still being obligated to the contract (Robinhood says my max loss is the premium I paid when I bought the option, so I cannot be obligated).

There are two parties to the transaction (a buyer and a seller) not three. There are four possibilities, depending on who is opening or who is closing their position:

BTO + STO

BTO + STC

BTC + STO

BTC + STC

Let's start with some proper terminology.

Buying a put or a call means that you are long the option. You own it.

Selling a put or a call means that you are short the option.

A covered call means that you own the stock and you sold a call ( + S - C )

A covered put means that you are short the stock and you sold a put ( -S - P )

If you have the appropriate option level approval and the margin, you can sell a naked call or a naked put ( -C ) or ( -P ). If you don't have approval for naked writing but you have approval for cash secured short puts then you can sell the put ( Cash - P ).

Who in their right mind would buy and cover the out-of-money side of the option just a few hours before closing?

An extreme example: If a just out-of-the-money naked call is near worthless a few hours before expiration, a takeover is announced and the stock jumps $20, guess who loses a pile of money?

What happens if there is not enough market activity to sell the option, could I be stuck with the option, having paid the premium, without the ability to exercise? If the open interest is 1 on the day of expiration, the option cannot be sold back to the market due to lack of interest, and I am on the out-of-money side--could it suddenly be assigned?

A long ITM option can always be exercised if you have the margin to support the position. You don't so this doesn't apply to you. For those that do have it, sometimes, exercising an ITM option (with simultaneous closure of the newly acquired position in the underlying) provides a better sale price than selling it.

The market maker makes a market for all options. If an option has value, there will always be a bid and an ask. You may not like the price but it will exists and you'll be able to STC the position.