Questions about Bitcoin Transactions
but it didn't tell me from which address the transaction was sent from


Indeed, there is no 'from address' in a bitcoin transaction. (More info)


  Am I correct, that when sending a bitcoin transaction, all of the amount from a specific address gets placed in the input, a part of it(the part which I specify) gets sent to the address I wish to send, and the rest gets transfered to a newly created address on the same wallet, from which the send operation was initiated?


Correct, inputs are spent all at once, there's no way to partially spend it, so you have to send some change back to yourself. The sendtoaddress manages that all for you.


  How is Blockchain.Info able to retrieve information from any kind of Bitcoin Transaction, while I, using a full Bitcoin Node, can only find transactions which was either initiated by the node, or which has a receiving address which is in the nodes wallet?


That's a lot of data that bitcoin core doesn't usually need or use, so it's not usually indexed or accessible by bitcoin core. It's possible to use the -txindex configuration option to index all transactions including those not related to your wallet. But blockchain.info and similar block explorers probably run their own databases of information rather than querying it from a bitcoin node every time, allowing them to do more complicated searches in the data.