Do I have rights for the properties even though I live in a different country and have not signed the divorce papers?

Yes but they may be hard to enforce if you do not come for court.

Your rights to the marital property will be determined by the court in the divorce proceeding. If you do not live in the jurisdiction, make certain that you have properly responded in the court case, are receiving all court notices, and are responding timely to those notices. If not, would be concerned that your spouse may enter a judgment with the court against you by "default".

Yes. Where you live has nothing to do with your rights.

It is useless to try to anwer this question because there simply are not enough facts to even guess what is going on. Rights in what properties? If there are marital properties we start with an equal division of them. There may be special equity. If you sign the divorce papers everything will probably be agreed upon, and it would become final. In order to get advise you need to give facts about the circumstances. You need to consult with an attorney concerning any legal situation. You cannot rely upon the legal advise given by non-attorneys. Hire one.

Generally yes, all of the marital property is in play, wherever you or it is situated. For specific opinions I would have to have all of the facts, good luck.