How is it possible for me to sell and buy on binance within seconds if every transaction has to be recorded in a block (and it takes about 10 minutes to validate the next block).
The trades you make on an exchange are not recorded on a block. Centralized exchanges have their own internal ledgers/databases to monitor exchanges made on the exchange. The only things which are recorded in a block are when you deposit or withdraw from the exchange.
Think of it like this. I send your department a letter in the post (making a deposit, which is recorded on the blockchain). The staff in your department spend some time drafting a reply, emailing it back and forth to each other, changing and editing it (internal transactions, which don't touch the blockchain). They then print it off their reply and post it to me (making a withdrawal, which is recorded on the blockchain).
How can it be that prices on all exchanges are more or less the same? Let's say, someone sells 100 bitcoin on binance for a price way below the market price. Why doesn't the price on this exchange drop far below the price on other exchanges?
Sometimes it does, but the gap rapidly closes. Very occasionally you will see a "flash crash" on one exchange, triggered by a single large sell off, a series of bots all triggering each other, someone missing out a zero when inputting a price, or something similar. The price can drop markedly, but it rapidly closes as users takes advantage of this lower price. The majority of trading on exchanges is done by other pre-set orders or by bots. They react almost instantly to any big swings in the price.