Both MetaTrader 4 and MetaTrader 5 are owned by MetaQuotes Software Corporation - www.metaquotes.net. MetaQuotes was established in 2000 and is currently headquartered out of Cyprus. It has offices in China, Singapore, Australia, Turkey, Pakistan, Thailand and Japan.
MetaTrader 4, released in 2005, is a fourth-generation trading platform which proivides algorithmic trading to large number of traders around the world. MetaQuotes provide what is essentially a 'white-labelled' version to brokers around the world. The brokers can then add their own branding but the base MT4 architecture is consistent between all broker offerings.
It depends on the asset class you are referring to. The Forex market is open 24x5. It's a follow the sun market which open at 5pm Sunday and closes at 4pm Friday. Timezone differences create market overlap where more than one market is open at the same time. Eg London Close/New York open, New York close/Sydney open. Indices markets vary depending on the asset - eg US500 is open from 9.30 (ET) to 16:00 (ET).
Generally when the forex market is closed MetaTrader brokers are also closed so the platorm will be online but there will be no incoming tick data received. This means indicators and EAs won't operate unless ticks are simulated.
Well that's a very big question. We put together a few basic videos to get you going. Here's the first one.
There are quite a few brokers who are providing cross rates for cryptocurrencies. Whether you can trade them will depend on your jurisdiction. In the UK the FCA banned trading in crypto derivatives in January 2021. If the area where you are based allows you to trade derivatives then there's no reaosn why you can't access the crypto market via/through MetaTrader.