Can you talk on the iPhone and use Siri with Monster beats headphones?

Yes.

The Monster Beats cables are fully compatible with Apple hardware. They have a mic to support voice actions and Siri. They also have all the hardware buttons for playing music and making phone calls.

I happen to own the Beats Solo headphones. This is what the packaging says:

"Made for iPod", "Made for iPhone" and "Made for iPad" mean that an electronic accessory has been designed to connect specifically to iPod, iPhone or iPad, respectively, and has been certified by the developer to meet Apple performance standards.

(also see MiF logo on Apple's website)

These minimum standards would include voice and button actions using the headset.

Yes.

You should be okay. The beats headphones mic is simply an extension of the built-in mic. Additionally, the hardware to filter out background noise is inside of your iPhone and so the mic won't make much of a difference. Can you do same thing with your standard Apple headphones, right? It's the same thing.

I personally use Klipsch ONE headphones with my iPhone 4. It works well with voice commands. I used my Apple earbuds with the new iPad before. Dictation works like a charm. So, yes, you can.