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If I have one program run through a proxy then turn on my vpn, will the vpn "override" the proxy?
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? 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?

Second question, any good program I can use to analyze my network traffic so I can test this myself?

Based on my understanding, yes, the vpn setting will override the setting of proxy. Therefore you cannot use both proxy and VPN at the same time. The reason of the slower speed of VPN is due mainly due to the encryption between the VPN client and VPN server. So you simply cannot enjoy the speed of proxy while the data encrypted by VPN.

Actually, I believe you CAN use both. The VPN connection will grab all of your network traffic and route it to the exiting VPN server while at the same time, your proxied traffic will travel through your VPN tunnel, exit at the exit server, then connect to the proxy server you have setup.

I have done it by using adguard premium app. In the settings of the app you can opt to monitor either https , or vpn traffic using adguard proxy server.So you are getting proxy speed for surffing , while still vpn running and protecting the rest of your apps. No root needed , just make sure to set proxy mode on manual when configuring wifi.Premium Adguard comes with default proxy server ,and you can get it free piratebay>applications>android. Look for cracksnow upload.

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.