On a web site where i have installed FreiChat, users are able to chat successfully with other fellow users who have logged in. But sometimes the following problems occur-

1. When a user logs in into the chat room, what he sees continuously in the chat box is fetching data message. It does not change eventually to "No user online" if there are no other users online or show the names of users online if there are existing users online.

2. After a user leaves the chat room and logs out, it takes considerable time for the off line status of the logged out user to appear to the user at the other end of the chat room. It would appear as if the logged out user is still online.

Please, how can these problems be solved?

The first problem may be because of the server speed.
The solve the second problem, please the the 'busy time' and 'offline time' from the backend.

Currently, the busy time out is the default 200 seconds and the offline time out is the default 500 seconds. I would like you to suggest values for the adjustment that you suggested in respect of the two parameters. What is the significance of increasing or decreasing the busy time out and offline time out?

well you will have test the time and see which settings you like for your site.
the time is the amount of interval between when the user is online to when the user goes busy -> offline.