If depends on the repeater many run WDS which requires access to router there are some that do not but it is hard to say which do not. You see many posts on this forum from people who cannot make them work for various reasons.
It should be obvious why they lose 50%. They must take the information and retransmit it this is twice the information. In addition since the wireless bandwidth is shared these transmission affect all the users using both the repeater and the main router. This will degrade the performance of the entire system for everyone even those that can get strong signal to the main router. Since interference causes retransmissions when it detects errors you now have the main packet retransmitted plus the repeated...