I can definitely provide you with information about potentially serious issues with the claiming of expenses by contractors via umbrella companies or personal service companies. (Google “National Contractors Project”.)
Are you actually using an umbrella company or is it your own company? I don’t see how you could acquire the use of a company vehicle through an ordinary umbrella company arrangement. If you want more useful information, you’ll need to provide more information in relation to your setup.
It is possible to use an umbrella company to buy a company car - you'll be subject to the standard 30% BIK charge on the original retail value of the car (less some discount perhaps). I would however doubt that the provider of the umbrella company would be interested in all the admin that goes along with it. If it is your own umbrella company then I don't see why not.
There is a reduced rate of BIK when you do serious travel (> 30,000 kilometers per year) but I'd pay attention to what torblednam mentions above re travel mileage and related expenses.
Probably yes. An umbrella company is one that you become a director off and the promoter looks after all the admin (for a fee obviously). You can google an umbrella company to get an idea of the costs and there are various levels.
Pros and cons of getting your own company going and you'll find plenty of comment about it on this website.
Worth noting that electric cars currently attract a 0% BIK rate, which can make them very attractive to purchase through your company, assuming they suit your usage profile and all that (lots of threads about that elsewhere on AAM).