But, ensure you adequately secure your VPS so that only your IP has access, or set up a VPN client on the VPS so that only clients with the proper credentials (i.e. you) are able to access it. The second method is preferred. If you don't do one of these, you will have an open resolver, which is highly undesirable and will likely get your VPS service canceled.
Is there any article with more details of consequences of having open resolver? Why would the service be canceled? can't we host public DNS servers on VPS services?
I'm considering using Wireguard with certificate to connect my phone, would it be enough on Security side and would 1 CPU 1GB RAM VPS be able to run it?
So, DNS server cannot be left open because sending queries is very cheap and would overload the server for processing all of them, and to provide public DNS server one needs a huge enough infrastructure?
Then, is a 1 CPU VPS capable of processing Wireguard for a handful of clients?
The answer to your question depends largely on four factors.
The maxmium Wireguard throughput of your VPS, measured in Mbit/s (known only by your VPS provider, if at all)
whether your VPS provider's internet connection does support that bandwidth, measured in Mbit/s ((known only by your VPS provider)
whether your own ISP supports that bandwidth, measured in Mbit/s (known only by you or by your ISP's plan)
the accumulated peak and average download speed by your handful of clients, measured in Mbit/s, which in turn depends on whether your VPS will handle all of your internet traffic or just DNS (known only by you, if at all)
Overall maximum throughput will be limited by the lowest value of the above.
If you are connecting to your VPS instance for DNS exclusively, then it is highly likely it will be sufficient.
If you are routing all traffic through it, you'd have to check the numbers.