Can anyone please explain me what will be the compatibility/communication issues of using media converter at one end and fiber switch at the other end.? if no, then will different brand of fiber switch and media converter will have any impact.??
As long as the two devices utilize the same network connection type and follow the standards, there should be no compatibility/communication issues. They should be able to work without problems.
However as Ron points out, there are other potential negatives to such a configuration. He mentions another point of failure, and I will also add that it can make troubleshooting a bit more difficult. For instance, most media converters are not managed (again as Ron pointed out). This means that you will only be able to pull statistics from one side of each of the copper and fiber links. So you may not see errors on traffic flowing in one direction on the link.
Also, link state is not always mirrored on media converters, so one side of the link (from the switches' perspectives) may look up while the other side shows down. You may see the link as up from the side you are troubleshooting and see outgoing traffic but no incoming traffic. This may initially lead you to false assumptions about what is actually taking place.