Yes. This is per calendar year, so you need to keep a total of business journeys. Once you're over the 6437km the rest of the year is at the lower rate.
Not 100% sure TBH but I believe anything reimbursed above this level is taxable to the individual, so you can't (say, as a director) pay yourself €1 a km indefinitely, for example.
If you're self employed and invoicing a customer, you are invoicing them for goods / services provided. As a self-employed person your motor/travel expenses are your own responsibility; if you are passing the cost onto your customer you do so by increasing the amount that you are charging for the service.
So I think the answer to your question is that you charge the same rate of VAT as is applicable to the type of service you are providing.
1. In theory you can claim a higher rate than civil service rates. However, you would need to get specific approval from Revenue. This is provided for in the Revenue statement of practice SP IT/2/2007 which is available on Revenue website.
2. Yes earlier miles are paid at a higher rate.
There is a website mapmiles.com which calculates the distance between points and your mileage expenses based on these civil service rates. You can also use googlemaps or the AA website to calculate distance.