Hi Usman,
In brief, yes and yes.
4 days in 1 month is what is known as a flexi-pass; you pay a bit more for your travel days, but in practice you get better value most of the time because you don’t have to use them consecutively, so none of them go to waste. From the day you activate your pass you have one month in which you can travel on any four days. So in your case you could use two days to get to Switzerland (though a one day trip is possible if you’re starting from London or nearby), and two days to get back a week or several later.
If you’re British you are indeed European, including for the purposes of Interrail (so buy this, not Eurail). Shortly after the Brexit vote our rail companies tried to pull out of the scheme in order to try and coerce foreigners from mainland Europe into buying a more expensive standalone Britrail pass, but there was quite rightly a massive outcry over this and they had to abandon their plans.