Thats just a bulb. A 400w hps requires a ballast and everything. U cant just put that bulb in any socket and expect it to work
To answer the other questions. They csn only detect it if their using infrared and even tgats insubmisable in court(in USA). Mines like $20-30 a month to run i think and yes u can mix cfls and hps. Put the hps as overhead light and cfls down low to get to the lower branches. I hear multi spectrum lights create dense buds
It gives the bulb its juice. Creates more power for the bulb being used... This is the light i got. Not sure of the price in £… http://www.htgsupply.com/Product-HTGSupply-400-watt-High-Pressure-Sodium-Grow-Light.asp
The ballast is very important, because the HPS bulbs are not like normal filament bulbs. Because of how they actually work (an arc of electricity excites sodium and mercury vapour to emit liight), they need to be supplied with a constant current, otherwise they will kill themselves very quickly. The ballast regulates this. It's similar to CFLs, and they do need a ballast too, but because they are very low power it can be built in to the base of the bulb which is pretty convenient.
Regarding cost, it depends on what tariff you are on with British Gas, but as a rough estimate... Standard tariff (single rate with a daily standing charge), you are looking at about 440 Watts (the ballast consumes a bit of power on top of the 400W bulb) running for 24 hours at a cost of 13.29p per kWh is about £1.40 a day, or about £40 a month. If you used 18/6 instead of 24/0 it'll be about £30, and obviously when you switch to 12/12 it will cost about £20 a month. More rough estimates, but if you were to say 6 weeks of veg and 6 weeks of flowering, you're looking at about £100 per grow, plus or minus £20 depending on exactly how long it takes and what light cycle you use. If you have two or three regular household CFLs going at the same time as your HPS, you want to add about £15-20 to the overall cost, or double that for a proper CFL growlight. BG fixed-rate prices are probably one of the most expensive on the market, so if you have duel fuel, pay by direct debit, are on a cheaper fixed-rate tariff, or on a duel-rate and already use up all your high-rate allowance every quarter, you could save maybe a third and bring the cost down towards £70. You can use the CFLs at the same time, all light is good light (more of less). If you're growing a few plants you can get the CFLs closer to them than the HPS, which might mean you can get more light to the lower branches or the periphery of your grow, depending on how you place them. If you have the CFLs at the same distance as your HPS you'd pretty much be wasting that extra few quid of electric.
Consider a 600w HPS dual ballast that does 600w? Mh at the flick of a switch and you'd junk those CFL's in a blink of an eye. 600w HPS = 1sq. metre or yard, good for 9. 3 gal pots to my blog and see the library peace "V"