1. Is car allownace considered maintenance and running cost of your private car OR employer contribution towards your new/private car?
Generally car allowance is taxed in the same way as salary, check with your employer though to confirm this is the case.
2, If car allowance is not running/maintenance, then employer would pay me only fuel cost of my business miles. Fuel card means employer would pay me approx 10p/mile i'd do for business while HMRC guideline says 45p for 1st 10,000 miles and 25p onwards. Can i claim tax relief at the end of the year? Let say If i do 40K miles an years with 20% tax bracket can i apply for tax relief of
(0.35x10,000x0.20 )+ (0.25x30,000x0.20) = £2200?
Yes - i am presuming you are not paying tax on value of fuel card purchases.
3. Am i missing somthing here? can employer define car allowance as running cost?
Its an agreement between you and employer with regard to things like this , unless your contract of employment stipulates anything they can pay whatever both parties agree whether thats 90p a mile - 2p a mile - or a chocolate egg each time you fill up the car. HMRC don't get involved and tax consequence follows rules laid out - ie if employer pay you less you claim balance from hmrc.
Note you and employer both lose out where you are paid car allowance and lower mileage rate rather than full mileage rate and lower allowance as you will be paying NI on the car allowance payment even if you claim tax relief direct from hmrc.
4. If i do not use company fuel card for my personal miles how would i prove at the end of year that i havnt used company fuel card for personal use?
You always need a full log of business miles - date / description / miles and basic vehicle details - something hmrc could fact check if they so chose.