Why are transactions grouped into blocks when put onto blockchain?
Blocks provide a way for transactions to be committed to the blockchain. They are what allow transactions to become immutable. By grouping transactions into a block, they become protected by the Proof of Work that the miner had to do in order to create the block. This means that in order for anyone to change a transaction, they must also perform the Proof of Work to modify the block too, and all blocks that come after the block a transaction was in.
Lets say we have just put a block on a chain and there are no blocks at the moment that users mine. At that moment how many new blocks will get created for users to mine? Will only one block-to-solve get created, or more of them?
If more blocks will get created (to be mined on), how will the miners distribute themselves on the blocks?
Mining does not work like this. Blocks are not distributed to miners to be worked on.
You can think of minining more like this: each miner creates a block, hashes it, and sees if it is less than the target. If it is not, they throw away the block and make a new one that is slightly different. They do that over and over until a block is found that has a hash that is less than the target. Miners will end up making quadrillions or even quintillions of invalid blocks until they get lucky and make on that is valid. Each block is unique and constructed by the miners themselves.