Using its own blockchain as a ledger and a DHT network as a storage layer

Are the git objects themselves stored in the DHT, or is it just (like a trackerless torrent) the connection information needed to find peers willing to send you those objects?

The object themselves are stored across the peers, not the connection information.

What prevents someone from using this to store backups of their harddrives, photos, etc, and consuming as much space as possible?

It needs an incentive model, like for every GB of space you provide you get a GB of space from peers.

There are proof of storage techniques. I already listed some references in the paper I am working on (https://github.com/gitchain/gitchain/blob/master/gitchain.te...)

Please could you explain why? Trackerless bittorrent is just as decentralized, and seems more scalable.

Does trackerless bittorrent provide a way to update a file ?

The git objects themselves are content-addressable (the key is the hash of the value) but you still need a unique ID that references the HEAD of this chain of objects. This id needs to be updateable.