In answer to your questions:-
(1) Usually 2x Turntables or The same number of CD Players (or a dual cd player), An Audio Mixer, an amplifier (at lest 2x 250W RMS) a pair of loudspeakers, headphones and Microphone are the basics of the Audio Equipment. Some form of lighting will also be required however, how many effects and what type depends on your budget. New Kit Packages vary from £700 - £2000 depending on your requirements, the type of mixer and the power output from the Amp & Speakers.
(2) Depends on what you buy 2nd hand, the make of the equipment and how much use it has had

, you don't really want to be buying somebodies ex hire equipment, or somebodies problems. You could pay £500 for a 2nd hand system which has had 4 years worth of use, when £800 would get you brand new kit with warranty. There are some real bargains to be had, equally there are some lemons

. When you buy 2nd hand make sure that you see the equipment working and check it over for potential problems. I think the time has come for me to write up a review on what to look for when buying 2nd hand

.
(3) Hmmm, since this forum is funded by a Sound & Lighting Retailer then this isn't the sort of question you should be asking here, it's not good for business to advertise your competitors as you knew when you read the rules! (The ones you agreed to abide by when you registered!

)
It's no secret that the Ebay Auction is full of 2nd hand Disco Equipment, and many forum members may have items which they wish to get rid of?, so maybe they can post up anything they have to offer on this thread?. Your local "Loot" publication may also list some complete roadshow's for sale locally.
(4) This is up to the individual D.J's really, its usually possible to hire equipment from a local retailer or another D.J (Yellow Pages) although the price can vary from area to area.
With regard to mentoring, again if anybody in your area wishes to offer you this courtesy (assuming your over 16) then I'm happy for them to contact you. Other basics such as advertising, and getting started is covered in great depth on the forum, although it may take an hour or so to read all of the advice. I agree and would recommend to anybody that the "mentor" approach is a must when just starting out since there are many things that can be described but not tought on a forum and those which you can only pick up through watching another D.J at work.