1. What is the tax deductable rate for hourly use of aircraft (e.g.
for cars it is $.36 a mile I believe)?

$0.99 or $0.98 a mile, can't remember which, there is a specific provision
for it

2. Is it better to own my aircraft personally (to prevent the
aircraft being owned by the company in the event of a lawsuit) and
then have the business (LLC) "rent" from me personally for a certain
amount? How much is this "rent" and is it based on actual costs or
future costs (overhaul, etc)? Taxwise I will have to declare the rent
as income if it is more than my operating costs, right? But the
business gets to claim it as an expense, right? But how to convince
the IRS of the actual and future costs of aircraft ownership?

In my opinion, you are better off spending money for adequate insurance
coverage than legal advice on how to shield yourself liability-wise. The
truth is that if you are flying on business, and sh*t happens, both your
personal and business assets are at risk no matter how you set it up.