whats the size of block headers ( minified blockchain) that ethereum light clients are using? how much is the size of the blockchain data required for the light clients to do a transaction and veryfy the data in contract?
Ethereum just released a light client public test :
The size of the blockchain on the disk is 600 MB today for homestead. For information, the actual size of the blockchain is 4,9 GB for fast sync and 21 GB for full, as of today.
Note, that as of today, there is no "trusted checkpoint" added, so it's built from genesis. Trusted checkpoint are trusted blocks header from which you'll start downloading your blockchain, a sort of --fast equivalent of what you currently have in Geth.
When they will be added, the size of the light client will be very less than the 600 MB.