does that mean bitcoin miners are the one completing transactions and filling up the blocks too?
Completing?
Miners are the ones "confirming" transactions. In Bitcoin terminology, "1 confirmation" means that the transaction is included in a block in the blockchain. Each additional "confirmation" means another block of transactions has been added to the blockchain after the block that includes the transaction being discussed.
Miners collect a set of 1 or more valid transactions such that the total number of bytes of data is less than the current block weight limit. Then they build an 80 byte header for that set of transactions. They complete a proof-of-work on that header, and then they broadcast the block of transactions (including the header) to all peers on the network so that everyone can add the block to their blockchain.
if yes, then what is now the job of those working at blockchain?
You mean "blockchain.info"?
That is a business that came a few later after bitcoin was created. They built a website that listens to the bitcoin network and provides information and statistics about the transactions that they see on the network and about their copy of the blockchain. They eventually also built a web based bitcoin wallet for people to use. They are not in charge of bitcoin, they did not create the bitcoin concept, they are not in control of the bitcoin blockchain, and there is nothing official about them. They are just a third-party service that chose a popular bitcoin related name for themselves.
How many transaction fills up a block?
However many the solo miner (or mining pool) wants to put in the block as long as it is at least 1 and the total size is less bytes than the current block weight limit