No problem! The only way to get any of the illuvium fuels is to purchase them from the fuel market place. You will need test Eth to do this. You can claim a small amount every 24 hours when you log in to the game. If you need more there are other 3rd party websites that can give you some, but you will need to be familiar with defi and using crypto wallets. You can also get some Eth by selling in game assets. If you capture the right illuvials in a stage 0 run you may be able to get some test eth to buy some fuel
After a while I stopped farming every single stone. I focus mostly on the different colored ones only for shards and rare resources. I have enough of the common items. With that I can farm and hunt illuvials at the same time
I do the same, but occasionally it's good to just smash out a few shard farming runs to refill your bags. You'd be surprised how many shards you can get in a couple runs like this