Rate-limit configurartion at the VIP Level and at the host Level

> 1- In a condition that we have a rate-limit configured on the server side, in this scenario load balancer will build the client side connection in the connection table and check for number for connection on the server side, if the number of connection are less than the connection limit then load balancer will build the server side connection in the connection table?

Your question seems to be confusing two separate things:

rate-limit - connections per second

connection-limit - total number of simultaneous connections

> 3- In which traffic condition or traffic type we have to use rate-limit configuration on VIP level and in which traffic condition we have to use the rate-limit configuration on the host level?

This question is easier to answer.

A pool member connection limit or rate limit is used to ensure that connections distributed to pool members do not exceed the capacity of those pool members to handle the load. If a limit is reached on a pool member, a new pool member can be selected that has not reached it's limit. There should be enough pool members available to allow this to occur. You may use things like priority groups to include slower pool members when capacity is being exceeded on faster pool members.

A virtual server connection limit or rate limit is an absolute cap on the traffic to the pool members, and (if configured) should reflect the total available capacity of the available pool members - in other words, the virtual server itself should limit the number or rate of connections so that the pool members are not overloaded or stressed.