How a block is defined (size, number of transactions)? While exploring the Blockchain.info charts, I learned that:


The average size of blocks is increasing (max=1MB).
The number of transactions in one block is also increasing.


After reading some related articles, is it right to say that


One block is defined (solved) by mining. If I have a super powerful computer, I can mine so quickly that one block will only contain one transaction. (I'm trying to understand if there is a link between the number of transaction and the mining speed.)
The transactions in the same block are not linked between each other. So miners do solve one transaction, but one block.
A block must satisfy the following conditions for it to be valid:


The total size of the block must be 1MB or less. 
At least 1 transaction called the coinbase transaction must exist. 
Block must satisfy proof-of-work.
Block must reference a valid block as the previous block.


There are some miscellaneous restrictions, but these are the main ones. What you called "solved by mining" is what's called satisfying the proof-of-work. What you called having at least one transaction is the restriction that the coinbase transaction must be present. I encourage you to read the specification to find out more.