#1
I would like some advise on a good power speaker frfr to use with hd500x, I would like two speakers with my budget for speaks £600.00p for home use and maybe small gigs ,
I would also Like to know If the Hd500x has stereo? and is all you need for stereo setup two speakers.
#2
1. If you want to do some light gigging, an 8" speaker would be a good start for projection and bass response.
Something like an M-Audio BX8 D2 pair is £199 and would likely do the job fine.
If you want something a little more upmarket, you can get a pair of Tannoy Reveal 802s for £350.
2. The HD500X does have stereo. All you need is either a pair of unbalanced 1/4" cables or a pair of balanced XLR cables.
#3
There are right and left outputs for stereo, and you can edit your user presets to send signals hard right and hard left *or* put them right in the middle if you prefer.

Here in the US, a good solution for would be something like a Carvin PM12A ($319 ea) for both home use and any amount of gigging you'd care to do. http://www.carvinaudio.com/products/pm12a-molded-2-way-12-inch-powered-loudspeaker-monitor These things weigh in at around 30 lbs, have a built in 400W RMS amplifier and a frequency response of 50Hz - 18Khz. You can, of course, turn them down as low as you like.

An option for the bedroom might be a pair of KRK Rokit 8's, which are powered recording monitors with an 8" woofer (seriously, plenty for a bedroom or den) and about 100W per speaker of built-in biamp amplification (divided 75W to the LF driver, about 25W to the HF driver). About $250 each, as I recall.
#4
I have a Yamaha Stagepas 300 which I play my Vox ToneLab SE directly through. It's served very well in a number of roles from home twiddling to small gigs with a 4 piece band. The current version seems to be the 400i.

Of course any sort of compact PA system should suit the job, but the Stagepas is nicely thought out in terms of portability.