how much cost a bitcoin transaction? My client asked me to use the bitcoin blockchain to store some photos hash as proof of existance.

I read that pulling this data on into the blockchain is not free

1) How much does it cost ?

2) Who gets that money ?
I suggest you look at opentimestamps. From the website:

A timestamp proves that some data existed prior to some point in time. OpenTimestamps defines a set of operations for creating provable timestamps and later independently verifying them. At the time of writing timestamping on the Bitcoin blockchain is supported, the format is flexible enough to support a variety of methods.
Anyone could realize a timestamp with the permissionless blockchain by paying the transaction fees, for your convenience we offer calendar servers that perform this operation for you. These servers are free to use and they don't require any registration or api key.