- Could I run both Ethereum and Bitcoin-Core on one PC ?
Yes if your hardware and software is compatible to all requirements. Please check both of them for their requirements.
- Are there any reason for not running both Ethereum and Bitcoin-Core on one single PC?
Yes, main reason for me would be security, especially if you run it on a server, where if you use it on your desktop PC, there should be no concerns unless you install any another software, some software could contain some malicious code or a bug (ie. of the one of both wallets) which might harm your pc or even steal your coins. In general, there are many ways how your pc can be attacked/infected. There have been several exchanges which did make that mistake to put way to many wallets on one server.
- Could there be interference as far as the internet access and ports, etc. ?
Yes there could be if you use for both wallets same port number in your configuration. If you do not make any change, they will use their default ports which do differ and would work properly. It could also always be that some another application uses defined port.