Hi there ammar87!
I second KevinIV.
You will need to compensate for the DC motor reactance and also depending on the maximum current at stall I am not so sure the power opamp will be capable of working out for you. At quick glance L165 has max output current of 3A which can be easily exceeded. The heat dissipated by the regulating element can be quite a lot, as well. For example, powering the system at 12VDC and operating the motor at low speeds (say 3V) with some load on it (say using 1A) causes the linear amplifier to dissipate 9W continuously. That means you will also need a decent heat sink.
Also, the DC motor brushes / commutator will output a lot of noise due to brush bouncing and mechanical switching from commutator plates (EMI). Some of that EMI is conducted some is radiated.
Long story short, to answer your questions:
1. I've used OPA549 by Texas Instruments for different applications, but non the less it is quite capable of delivering high current into a load (up to 8A continuous and 10A peak). You will still need a heatsink. I could not open the motor link you provided.
2. I am not aware of one. Most people use PWM due to the high power efficiency. Noise can be reduced by reducing the switching frequency and reducing the slew rate of the rectangular waveform. That sacrifices efficiency but reduces noise due to high speed switching.
3. It depends if the amplifier is connected to bipolar power supply. If it is and the DAC can output bidirectional voltage then yes. At the very least you will need to connect a snubber across the motor (resistor and capacitor in series) to compensate for some of the noise and the motors inductive reactance.
Hopefully that was not too much and helps you