Can I setup home recording studio all in 1 room

you have too much latency in your setup. Try using ASIO as your audio engine in your recording program. Also, shut down all unnecessary programs running on your computer to get better performance.

there should be some kind of main l/r out or control room out on the mixer. that'll plug right into the bxa's.

It is likely you do not have the levels set correctly and are over driving the mixer. Reduce the trim settings using the PFL buttons and monitor the level indicators to insure you are not clipping.

With a condenser mic you CANNOT have any speaker in the room that the mic can hear of course. These mics are so sensitive. Your mixer and monitor speakers and recording will be in a separate room from the soundproof studio typically.

To monitor the system anywhere in the same room as the mic you MUST use headphones that do NOT leak sound or you will get feedback and distortion.

There are a number of configurations for a mixer like the 1832, the most common are PA system and Recording system. There are Main output jacks which carry the mix as summed in the main faders. These in a PA system would feed the pa amplifiers which drive the house speaker system for the audience. These connectors are XLR 3 pin type on the rear, intended for professional pa amplifiers which use balanced +4dbv line input level. Amplifier which have 3 pin XLR connectors for input signals can accept that high level signal. For home style HiFi amplifiers, the signal level is nominally -10DBv and balanced or unbalanced signal lines with 1/4in diameter phone plugs which are connected to the mixer by way of a second set of Main output connectors which are 1/4in phone jacks. Use whichever amplifier input level your amp has.
If you are not using it as a main PA house mixer, but using it for recording, the main output connectors go to a 2 channel recorder or computer sound card recorder. The power amp and your monitor speakers are connected to the connectors labeled "Control Room" (CTRL Rm). These output are useful for recording because the signal through the mixer can be monitored from several buses, Solo, main mix, selected by buttons provided. The buttons only affect the signal heard through the control room monitors, and not the main output which only sees the main mix so selecting "solo" does not interrupt the signal going to the recorder while the engineer in the control can be checking other signal paths through the board.

I suspect the problem is with the software setup in your PC. Verify all the options and also verify that the AUDIO system is assigned as stereo and assigned to the Lexicon for both in and out... Also check any "PAN" control settings. There is a possibilty that the Alpha has a dead channel...

Try putting a stereo signal into the 1/4 inch jacks and see if both record... if NOT then take it for repair under warranty... I had a Lexicon Omega that had a problem myself... warranty repair...

Try asking here:http://www.korguksupport.co.uk/page.cfm?pageid=370. Hope this helps.

We're talking about audio recording. If so you must conntect your piano by using the L + R outputs with your sound card or mixer line inputs (that's how I do this). USB is ok if you want to use your piano as a master keyboard (MIDI). Another important thing is that you must have an additional application installed called sequencer ( for example Cubase Sx, Sonar...) which will let you store your digital music. I'm not talking about the proper settings of them because it could take a day or so...:)
Overall, you will have to learn a bit about the home studio, home recording techniques. There are tons of informations on web. A great thing is that you can use your CP33 as a master keyboard to control additional virtual instruments (VST) or for example play different piano samples (check Synthogy Ivory). Possibilites are endless!

Regards
Radek