Any way to see all my current total stats (regen, resistance, armor rating, etc) in Skyrim?

The Windows firewall is just fine for most applications. As with running any server, start out with a default deny policy and open up only the ports that you need.

Perhaps the more important question is whether or not your application software is secure...

The Windows Firewall is lean, mean, and does its job well. I doubt it would affect your throughput, and I'd trust it over any 3rd party software firewalls. ErikA is right in that you start with a default deny policy (preferably including outbound traffic also) to minimize your attack surface.

However, the benefits of a hardware firewall should be understood, since relying only on a software firewall isn't a best-case scenario. Even if you can't use one, it will help you understand the pros and cons of each ("Why should I bother having two firewalls???")

You can use the following statement: There is no unit vector field $v$ on $S^n$ that is anti-symmetric with respect to the central symmetry of $S^n$.

This theorem holds because if you would have such a unit field, then you would have a homothopy from $S^n$ to $S^n$ that connects the identity map with a map from $S^n$ to itself that factors through a map to $RP^n$. But any such map $S^n\to RP^n\to S^n$ has and even degree (i.e. the degree can not be $1$).

Now if you accept the statement, you can reason as follows.

Denote by $C_{\varepsilon}$ the set of points on distance at most $\varepsilon$ from $C$. It is sufficient to prove the statement for each $C_{\varepsilon}$ and then take the limit $\varepsilon\to 0$. Now, $C_{\varepsilon}$ has $C^1$-smooth boundary, i.e. at each point of $\partial C_{\varepsilon}$ there is a unique supporting hyperplane.

Suppose that for every segment $[x,y]$ that passes through $p$ and such that $x,y\in \partial C$ the supporting hyperplanes $P_x$ and $P_y$ intersect. Then chose unit vectors in $P_x$ and $P_y$ at $x$ and $y$ correspondingly, that point exactly towards $P_x\cap P_y$. This will give you the desired vector-filed (anti-symmetric with respect to the involution of $\partial C$ that exchanges the ends of segments passing through $p$).

I never saw the book so I don't know if this is the solution that is expected in this book