I have a PMP2000 with 2 passive Peavey loudspeakers and 1 Powered Sub which I connect to Monitor.

You have two monitor outputs, each controlled by a fader. Plug the amp(s) you will be using to power the monitors into these, connect the monitor speakers to the amp(s) and you're set up and ready

As opposed to front of house? If you want separate amplification of a monitor system then use either the aux send channels or sub-channel outputs or control room outputs (but check these are not amplified already) connected to a separate amplifier to power your passive monitors

This mixer will run 2 8 ohm cabinets per side, if this is an older unit, it has only one NL2/combo jack per channel....with the button on the front panel in the Main Monitor position you can run 2 main cabinets and 2 monitor cabinets, you will have to daisy chain your speakers.All speakers powered from the back of the unit must be passive, no powered speakers.....if you want to use this head just to run moitors and run a pair of powered mains then connect the jack on the front that says main out to input of your powered speakers, hopefully your powered speakers can be daisy chained at low level, then if you want to use the 8600 to power only monitors, get a 1/4 in y cable and plug it into monitor out on the front of the mixer and then plug it into PA 1 and PA 2 to the right there and both sides will now be the monitor mix from this mixer and it will run 2 speakers per side, as long as the cabinets are 8 ohms.

The speaker connections are on the BACK and are "Speakon" connectors... These are special plugs and these apparently can also accept 1/4 inch plugs. It appears that the MINIMUM impedance should be no less than 4 ohms, NOT 2 ohms. One of the back connectors is for the mains, the other ois for the monitor soeakers. The FRONT connections are line level which doi NOT drive speakers,

First off it's outputs to your speakers. If you had an extra set of powered or amplified speakers you could "Y" cable your speaker outputs. Your passive speakers won't work without an amp. You really need powered speakers or an amp for your extra speakers. (if you had powered/amp'd speakers you could run them off one of you "aux" out for monitors. Do not daisy chain your speakers connecting twi together, you'll change the resistance/ohms and damage your speakers. Trust me, I do this for a living.

Yes you can - but do not use the loudspeaker outlets on the rear panel.
There are a variety of outputs on the front panel (bottom right as you look at it).
You can use the main output,  or monitor  send - (for monitor you may need to use the relevant 'send' switches on each channel to send signal to these outputs. 
You should also turn the power amp switch to main only (not main + monitor) so that the internal power amplifier is not connected to the monitor socket
You could also use the record out RCA (phono) sockets on the Peavey to connect to the CD / tape input on the main mixer.
You can download a pdf of the manual from here for more informationhttp://www.peavey-eu.com/index.php

You didn't mention what brand powered mixer you have, HOWEVER MOST powered mixers also have a line level monitor and main output jacks. These are almost always 1/4 inch jacks. In any case you should be using BALANCED lines to the powered speakers using either XLR or TRS connectors on the ends. Please tell us what powered mixer you have so we can give you better answer regarding which connections to use. IF for some reason your mixer does NOT have line level outputs, you can use a high level Direct Box to condition the powered outputs to be sent to the powered speakers..
Also make sure ALL your interconnected equipment is powered by the same receptacle or source to avoid damaging due to ground bounce on utility lines and circuits. This often means running an extension cord from the stage where the powered speakers are along with a snake of the audio cables.

The monitors will have to be POWERED monitors with built in amps.

You can simply use a wye splitter cable to drive the two monitors. Run the cable from the mixer to one monitor and put a wye cable and an extention to the second powered monitor speaker.

You run one or more of the AUX outputs to an amplifier then to a passive monitor, OR if you have powered monitors then you just run the AUX's as needed to the powered monitor(s)

You then adjust the "AUX" mix for each channel input to each of the AUX you are using for the monitors as needed.