Hello!
Question 1:
The Arduino Mini (v04) is being installed and wired according to the diagrams on the pages for the USB device and the actual Arduino pages. (Statement first, question now.) Are the Tx/Rx points on the bottom left of the device the same ones as the pins also marked as such?
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Yes. See the schematic: http://arduino.cc/en/uploads/Main/arduino_mini_schematic04.pdf
Your USB-to-Serial adapter will likely need a driver installed. See http://arduino.cc/en/Main/MiniUSB
Hello!
Understood. I've already explored the schematic, seven or eight times since buying both two years ago, Saturday. However that schematic is out of date. This is an ATmega168 based device, ideally it should be a 328 based one, but that's what the vendor had available. 
I meant regarding the Tx and Rx positions on the middle left of the device, and the pins. Are these the same as the connections on say an NG?
Reason why I chose that one, rather then the 2009 [Duemilanove] design which is what I also bought from the same vendor, is because the NG is mentioned on the pages for connecting the Mini to the computer system which the chap who wrote that page had on hand. Arduino Playground - ArduinoMini Here.
Gregg (doctorwho8)
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I guess I did not understand your questions. 
"I meant regarding the Tx and Rx positions on the middle left of the [Arduino Mini v04] device, and the [TX and RX] pins [in the near,left corner of the Arduino Mini v04} . Are these the same [ATmega pins] as the [RX and TX (also known as digital pin 0 and digital pin 1] connections on say an [Arduino] NG?"
If I understand this question correctly, the answer is YES. The TX and RX pins on the Mini work just the same as the TX and RX pins on the NG. A sketch written for the NG should work the same on the Mini.