I think your Arduino will do what you want, but with a bit of modification to the layout, as RuggedCircuits mentioned previously.
Connect your Arduino to your computer via USB. You can use basic Serial commands (provided in the Ardunio reference section of their documentation). If you have the FTDI USB cable, then when you plug in the Arduino, it shows up on your computer as a new Serial port. Programs on the computer can send and recieve serial data this way.
In order to handle the real-time aspect of your question, I would reccomend you implement a timer interrupt to check for data in the serial buffer. You'll have to implement a bit of flow control and command parsing, but that's not too difficult.
No, TTL is not the same as RS232. This is a common misconception. RS232 generally means it uses +/- 12V logic. You might damage your board if you tried to connect these directly to your Arduino. TTL generally means 0 to 5V logic. You can get converters to change RS232 to TTL, but it's unnessecary if you have the FTDI USB cable, since USB runs on 5V logic anyhow.
The boards (and I'm not sure about the nano here) use pins 0 and 1 for RX / TX for the hardware serial port. These pins are shared with the USB -> FTDI Serial connection. You can use software serial and use other pins for RX / TX if you need additional serial connections to the same microcontroller.
Once you have your connection with the computer established, use the analogWrite() function to create the PWM for your motors. The Arduino doesn't push enough Amps to drive most motor circuts, so you wouldn't want to directly connect your motors to the analog pins. Doing so might attempt to draw too much current through the uC, and burn out the chip. Instead, you'll want to use a transistor (or transistor package IC... or H-Bridge. $2.50 for 4 transistors in a chip). This allows you to control a larger power supply... using TTL logic levels. The transistor effectively switches on or off the larger power which supplies your motors.
I may be incorrect on this part, so someone correct this if my thinking here is flawed: There may be significant resistance that could impact the signal from 30m away. So you probably don't want to use the TTL power straight off the uC board to span the distance. Instead, I would use the transistor and power supply close to your microcontroller, and have the larger power flow down the long wires to the motors. This way, you're sure that the PWM signal won't have trouble switching the transistors. There may still be some power loss across the distance, but it will probably be sufficient for your task. If not, there are othere ways to boost the power again if needed. (ie: stick another transistor package with another power supply as a repeater down the line)