Am I permitted to claim the difference in the amounts that were spent on the company's debts before I joined it, and do I bear the losses when he was responsible for the management?

If what you paid is considered your capital and your contribution to the company, and the company incurs losses, then each of you bears the loss in their capital proportionate to their share, for "loss is borne in proportion to capital." And the fact that your partner is responsible for management does not make him a guarantor of the loss unless he was negligent or exceeded his authority.