How and where to pay in bitcoins into online wallet if I have address and ID I just found my "old" wallet.dat.
Is it possible to "send" it to an online-wallet in order to avoid downloading the whole blockchain again?
Or can I do it directly because I have the Address and ID of the coins?
I just found my "old" wallet.dat. Is it possible to "send" it to an online-wallet in order to avoid downloading the whole blockchain again?


NO. In fact, any service that asks you to transmit your wallet.dat file is most certainly a scam. 

A wallet.dat file contains a collection of private keys, which are what is required to spend your bitcoins. So if you would like to use a different wallet without syncing the blockchain again, then you will need to dump the private keys out of your current wallet, and find a wallet that lets you import (sweep) private keys into it. 

You can use a light-wallet to do this, rather than trust an online-wallet. You may be interested to check out the list of wallets on bitcoin.org, but remember to do your own research to ensure that you are downloading reputable software from a reliable source.