Transmitting and receiving on the same frequency is called simplex operation. You should use simplex operation instead of a repeater whenever a contact is possible without using a repeater so the repeater will not be tied up unnecessarily.
If you are talking to a station using a repeater, you could find out if simplex communicate is possible by listening on the repeater's input frequency and seeing if you can clearly receive the station.
The RST used in a signal report means Readability, Strength, and Tone. The meaning of "Your signal report is five nine plus 20 dB..." is that the relative signal-strength meter reading is 20 decibels greater than strength 9. The meaning of "Your signal is full quieting..." is that the received signal is strong enough to overcome all receiver noise.
The procedural signal "CQ" means "Calling any station". What is the correct way to call CQ when using voice is to say "CQ" three times, followed by "this is," followed by your call sign spoken three times. You should answer a voice CQ call by saying the other station's call sign once, followed by "this is," then your call sign given phonetically.
A QSL card in the amateur service is a written acknowledgment of communications between two amateurs.