How a block is defined (size, number of transactions)?
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.