If one user made a buy and a sell order at the same time, would they be matched with each other or remain pending?
On "real" exchanges Trading Against Yourself or Wash Trades are usually forbidden. Either by a real time check when you enter the second order or after the fact with fines by the oversight agency.
As Bitcoin Exchanges are not regulated, it's their choice to either block you from doing it or not (earning fees for the exchange).
The spread is pretty wide, so it will probably cost you quite a bit of money to do this on a meaningful scale.
Depends on which exchange you use. Those are all internal policies not used by the Bitcoin network.
The proposed scenario doesn’t make sense to me. If you would make a buy and sell order as market orders at the same time, you would lose money. If they were matched with each other, you’d buy from yourself, paying what you earn and losing the trade fee. If they were not matched with each other, your buy order would be the best for the moment, and your sell order would be matched with a lower buy order afterwards (or vice versa).
So, if you’d have a buy and sell order open as limit orders at the same time, you’d open them at a spread: e.g. buy for $5 and sell for $6. Those two orders would be unmatchable though. For them to be matchable, you’d have to open them at e.g. buy for $6 and sell for $5. Then you’d lose money on every trade though, and that would be stupid.