Well that's simple.
Basically VPN plugs your device in to the end point as though it was physically there, with a bunch of complications and variations around this theme. All traffic from your device now goes across the VPN and through that end network. VPNs can also be used to link networks together in to a single private network, hence the name VPN.
So..
Home VPN via your router makes it as though your phone or whatever is actually at home on the home network hence WoL, Web GUI etc work, even share drives and the like although that can take some tweaking.
A VPN service is a bad idea for privacy and security except for streaming because it can fool services to think you are in whatever country. But at the cost of being at the mercy of that remote VPN service not being evil and intercepting or manipulating your connection.
However in dictatorships and Islamic theocracies VPNs are hugely popular to bypass censorship or being executed for just browsing something "contraband". However if privacy and security is a concern then properly using TOR may be better. That's a whole other topic. A commercial VPN is not secure or private unless that's a better option than execution by your friendly local Islamic theocracy or dictatorship.
But VPNs are used for steaming because it can route you via countries to access streaming not available in your home country, or obfuscate P2P (which is a dumb idea, because torrents, P2P etc are just always a really stupid idea as they necessitate running servers, opening yourself up, and leaving trails a mile long about what you're doing, as well as uploading which is just the legal ticket needed to sue you big time).
VPN traffic is encrypted and only visible to the end point, not along the route where it's just an encrypted stream.
Home or work VPN is used to securely connect you to that network.
Once you're connected to it, it's as good as being physically on that network. Hence rendering WAN access unnecessary.
VPN has FAR stronger authentication such as certificates and other options, plus you can (should) move it to a non standard high port.
As for protocols OpenVPN is fine. Don't waste your time or sanity on the others.
Now.
You have dynamic DNS set up, well done. Now go to the VPN tab and set it up with a STRONG password.
If you are using Android, pay for the "Open VPN Client". It's a paid app but brilliant. I now have it set to auto connect when I leave the house. As a pleasant side effect, many free WiFi hotspots also now seem to work without signing in as perhaps they don't block my high port (idiots).
That's another thing.. NEVER EVER use free WiFi or basically any hotpot without VPN. It's trivial to set up a fake spot and sit between you and your bank or whatever. Don't risk it. VPN cuts all that shirt out, eg when you are travelling.
But just use the standard / auto settings for now and export a config file to all your devices. I'm not sure if a unique account is required for each device but make one die each anyway.
Then practice connecting with WiFi off from home or from your mobile cellular network (so you are "external"). This way you can easily tweak settings if any issues.
Once you're happy with it then you can gradually tweak settings to make it more secure eg custom high port, stronger authentication and encryption etc.
But even basic out of the box VPN is light years ahead of WAN access with simple hackable exploitable password.
And then you can Web GUI in and WOL to yours hearts content.
More complex stuff such as apps, share drives etc may take some work, but Web GUI access should easily work out of the box.
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