Revenue will definitely have a problem with your 'sole trader' status. If Revenue deem you an employee, they have the right to assess the company, you or both for any taxes they deem should have been paid.
Expense deductions are on a receipted basis for petrol etc. You should do an analysis of business mileage v total mileage and keep a very good diary to back up your business mileage. This will give you the % to allow.
The VAT status of the company you work for is irrelevant. You have to look at your 'trade' for your VAT responsibilities. So you will charge VAT and the company will have no right to reclaim the VAT.
Yes, use standard rate bands and credits for working out salary (you will not get PAYE tax credit).