I have a very limited budget, can I find a good MTB under £500?

First off this is the category for Motorcycle Protective Gear. The Bell Sequence Mountain Bike Helmet in matte black is not DOT approved for Motorcycle use. In any case the serial numbers are 2038082, 2038083, and 2038084 for small, medium, and large.
http://www.thebellstore.com/product/bicycle-helmets-bell-mtb/bell-helmets-bicycle-sequence-matteblack.html

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Neither screw is for mis-shifts. Those are limit screws for the largest and smallest cogs. Tweaking the cable tension will usually bring in the indexing...

http://www.parktool.com/blog/repair-help/rear-derailler-adjustments-derailleur

It sounds like your cable is/was a smidge too tight.

depending if you have a ajustment on the bowl you will need to ajust to get the right mixture if this will not fix your problem then you will need your carb rebuilt

before building a pc you need to know your budget bec. parts have different prices, high ends are more expensive, if you buy expensive parts with limited budget, you would end up short in cash

yes but you need to go to the machine shop in your area