Can i connect the pv 112 to the pv 118 subwoofer since the powered mixer i bought it only has 2 main outputs? The powered mixer I bought is the PV XR 8600D powered mixer...

We'll need the make and model of your mixer in order to help you.

You would come out of the Main output on the front of the mixer into the line in on the Bose.

You may find this site useful- L1 Unofficial Performers Guide

You can hook'em up utilizing the front low-level main outputs of your peavey684 to your headphone amp inputs, this should do the job satisfactorily.

Using TRS (balanced audio interconnect cables) go from the main output on the top of the panel to your amp inputs. MAKE SURE the amp is powered from the same receptacle as the mixer to avoid ground bounce and possiblle damage to your units.

Peavey uses a protection network and sometimes it gets blown when too much power is sent to the speaker. The speaker may be blown however. Peak power for this is 800 Watts and 400 Program... That is NOT RMS power. Make sure your amp is no bigger than 300 Watts RMS driving this. If you are REAL lucky, maybe a lead has fallen off the speaker... Open the unit inspect and test the components.

First of all confirm if the speaker impedance is not lower then the recommended Ohms at the back of the Mixer speaker socket.You can use an 8 Ohms speaker on a 4 Ohms amplifier but not vise versa .
Next see if the fan on the mixer works. If not the Amp is getting very hot and this will lead to unwanted distortion. You can confirm if its a heat related issue by playing the mixer at low volumes for more than an hour and see if it distorts.

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

In case you don't have one, here is a link to the manual:http://www.peavey.com/assets/literature/manuals/80300573.pdf I don't know if you are using a separate crossover between the mixer and the amp but here is the simplest explanation.I just reread your question and I don't even know whether you have a Peavey amp. Run proper cables from the main output of your mixer to the main inputs of your power amp.They will be 1/4"shielded cables or Balanced XLR cables. Do not use unshielded speaker cables to hook the mixer and the amp together.Run speaker cables from the speaker outputs of the amp to the input jacks of your speakers.Make sure the impedance of your speaker cabinets equals or exceeds the impedance rating marked on your amp. Here is the link to the newer model PV2600 manual:http://www.sweetwater.com/store/media/pv2600_doc_manual.pdf Don't use Speakon cables unless your speaker cabinets are equipped with Speakon input jacks. Banana plugs aren't as solid a connection as the binding posts are.

It should be able to do this. You would need to put each type speaker on a seperate side and then use either an elctronic crossover or an EQ set to pass only lows into the side for the subwoofer to block sending highs to the subs.

Hi there,
you can run one amp from the main out puts and the second amp from the CTRL Room out puts. The CTRL ROOM are outputs that are linked to the same bus as the master fader. This will work fine...
Best of luck