I'm using Infura API for initializing IPFS. IPFS uses garbage collector to clean 2 weeks old unpinned data in public gateway. So, if I'll pin my hash is it possible that IPFS will still delete my information from server because I'm using public gateway?
The doc [https://docs.ipfs.io/] mentioned that pinning an item is essentially marking it for the garbage collector not to delete it, so it will not be deleted.
if i will pin my hash is is possible that still IPFS deletes my information from server because i am using public gateway
If using public gateway, more likely it will be deleted. This is similar to how BitTorrent works, there needs to be at least one seed for data to be available to the network. Just like with pins, every node decides what content is fetched and seeded (co-hosted). Since you are on Public gateway, it is most likely to be deleted.