I have one program run through a proxy then turn on my vpn, will the
vpn "override" the proxy?
No, The VPN is more like a Network Adapter (or a virtual "network card" if you like). So if the VPN is on it is possible for the proxy traffic to go through the VPN (not the other way round - at least not when you do it on the same machine).
The case is, I want all my traffic to be encrypted over the vpn but I
want the speed of the proxy in this one program and still be encrypted
by the vpn, is this possible?
If you insist on using the VPN, then the final network speed that you get would be limited by VPN and the speed will be at slower of the two speeds (and in practice, the final speed you end up with will be much slower than either the VPN or the proxy alone).
Can I run this one program through the proxy and still have the
traffic encrypted through the vpn at the same time or will the program
using the proxy be unencrypted?
As I gave the example earlier, your VPN is like another "Network Card" (LAN Interface) except that its virtual. Thats the best analogy that I can give.
Therefore, you can use a proxy or even another VPN (tunnel within a tunnel) for all the traffic from your computer.
This is pretty much standard and we do it sometimes within larger organizations (for added security).
However the price you would pay with would be a drop in the speed of the connection, and this gets worse the more VPNs/Proxies you put in the way of the traffic.
So in other words, if are trying to add a proxy for "speed", no, it will not solve the problem since the limitig factor will be the SLOWEST passage-way the traffic encounters in its way to the destination (SO if the VPN has a lower speed, it would not make the fact that you added a proxy to the setup, any faster).
Second question, any good program I can use to analyze my network
traffic so I can test this myself?
There are many tools. For a non-professional the easiest but at the same time, a tool that that would give you significant insight into the process would be Fiddler.
If you really want to dig deep, then Wireshark is one of the tools used by professionals.
You did not mention the platform that you are on, but here's a list of other tools if you do not like the two tools that I mentioned above.