IPFS hosting files for free

Can I store files on IPFS for free & forever, like its possible with https://nft.storage/?

Hi @LukeSamkharadze, and welcome to the Infura community!
You can always check out our pricing page for pricing information, but we will continue to offer a free Core IPFS offering with 5GB each of storage, data transfer up, and data transfer down.

The thing is, I did not create IPFS account, I just used this URI

const file = ... ;
const ipfsClient = create('https://ipfs.infura.io:5001/api/v0');
const ipfsHash = (await ipfsClient.add(file)).path;

So, how many files could I pin this way, does it track my IP to limit file submissions?

We do not currently limit the file submissions, but that will be deprecated as soon as our IPFS Beta ends. Once that ends, you will need to sign up with an account and the limits will be enforced.