who is responsible as international court to solve economic conflicts between countries and is it obligatory?
As far as I am aware, there is no "general" international court for economic affairs.
The ICJ (Interntaional Court of Justice) is the judicial organ of the UN, and it in fact decided few cases with economic background, but usually in the context of other questions of international law.
The closest to what you are looking for is probably WTO dispute settlement system, which is described here: https://en.wikipedia.org/wiki/Dispute_settlement_in_the_WTO
In theory, it is for WTO members only, but in practice, 96 % of global trade is covered under WTO.

Other possible court is the International Court of Arbitration: https://en.wikipedia.org/wiki/International_Court_of_Arbitration
It has no clearly defined jurisdiction, instead, the parties must agree to bring the case to it, but it is becoming increasingly popular.

Last, but not least, an ad hoc panel can be established specially for given dispute.