Understanding Transactions, Mining, and the 10 minutes block solved

I’m not entirely sure if the questions I have regard to Bitcoin all relate to each other?

How do miners decide how many transactions they should have in a block in order to mine 1 bitcoin? When miners compete to find the “nonce” that has the smallest possible hash number, would it be faster/easier to find the “nonce” if there are fewer transactions? Or do miners try to pack as many transactions (up to 1 mb of data) into a block so they can get the most fees?

Do all miners try to solve a solution where all the transactions should be the same in a single block and everyone’s trying to compete to finding the nonce and hash? Or is it random, and its just whoever finds a hash the quickest, saves those transactions and adds it to the blockchain?

Also, I noticed looking at btc.com, there are blocks being mined less than 10 minutes back to back, I thought it needs to be 10 minutes to be mined?

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