In my country there is nothing like Islamic financial system. Could it be unlawful Islamically if one make use of the conventional financial system?

Everyone makes use of the conventional financial system. If you buy dollars and save them then sell them later when the price goes higher, you're making use of the financial system; but that is completely legal Islamically and socially. On the other hand you can take a loan with 10% interest (Islamically illegal) and reloan it to someone with 20% interest (Also Islamically illegal), that too is socially acceptable and is making use of the conventional financial system! The main guideline to which we should refer is what Allah allowed and what He condemned. In short, if it conflicts with what's allowed or leads to personal or social harm, then it is illegal Islamically. Interest is REBA in Arabic, and that is Islamically Illegal. Commerce on the other hand is perfectly fine as long as all parties agree to the terms. Reba is lending or borrowing money with interest requested by the lender. If interest is offered by the borrower, but not because of a need, (in my opinion) it is not Reba, but a business commercial deal, or a gift associated with returning the debt. That is my honest opinion, and Allah knows best! :) Best wishes to you afterall.

I do not know, I am not Moslem.

I think it depends on the transaction itself. I mean if it has anything to do with "interest" (which is just a cover-up name for "usury" no matter how low the rate is), then surely it is unlawful in Islam.