You can easily complete the Warehouse with green equipment, as proved by thousands of players. We recommend you to learn the game mechanics and balance better, there is no location, quest or enemy which can't be done without payments.
You don't have to buy a backpack. You can get the bigger backpack from the daily login rewards and once you reach 62 level you will be able to craft it on your own.
You've misinterpretend the answer of the support team. The log files are used to confirm if there was a problem or not. Your logs confirmed there was no bug in your situation.