Typically, a proxy server is located between you and the internet, like in the diagram below:
In this case, the connection speed between your devices and your proxy server will be limited only by the local network speed (usually ethernet or wireless). The main bottleneck here will be the proxy's processor/RAM performance.
This setup is not mandatory per se: the proxy can be located elsewhere. However, in this case, your data has to go through your internet connection first. It will flow from your computer to your modem/router, then to your phone line and then to your ISP (assuming you use ADSL).
In this other case, the connection between your devices and the proxy will be limited by your ISP. As you can see in the image, you are still connecting to the internet using your ISP, just like before setting up the proxy.
Actually, if you set a device on your friend's house as a proxy, your internet experience might even become slower, as you won't be able to take advantage of the multi-routed nature of the internet, as each connection will, obligatorily, pass through your friend's proxy (even if there was a much shorter and faster way elsewhere).
The bottleneck here will be your friend's connection. Your internet usage will now be subject to his latency, lags, pings, etc. Even more so in the occasions where your friend might be using his own connection.
That will be even more pronnounced if you set all the data from all your devices to use this proxy (not to comment on the inconvenience of doing so on every device you might own).
The only scenario where you'll benefit from it is if the connection from you to your friend is really fast, but the connection from you to more distant destinations is really slow, and the connection from your friend to these distant destinations is really fast. Your ISP will only see the local end of the data stream, and it will be served fast by the proxy.
However, I'd favor more a VPN than a simple web proxy: a VPN would reroute all data, while "proxy" usually refers to a web proxy, that deals only with web pages and other browser data. With a web proxy you need built-in support for every software you plan using (browsers have it, but online games not). When a VPN is active, it usually applies to the OS as a whole.
You can set up an OpenVPN server at your friend and connect there using a VPN client. Or you can hire a cheap server on your country just for it, I pay less than USD 15 / year for one, the specs required are really low.
