Ahoy and welcome.
Yes, the site will be open on "walk on" days. The pricing on that is for people who have their own gear: gun, eye protection, and BBs. Some sites have got back to really meaning "walk on" as in, turn up, pay and play. Some (many/most) now require pre-booking for "walk ons".
If you haven't played before then you'll want a rental package which will cover the above, so you can see if you enjoy the experience without spunking hundreds on a daft toy first. These are always pre-booked as the site will have limited amounts of rental guns. They tend to run £20 - £25 more than a "walk on", which looks expensive, but since you'd go through £10 or more of your own BBs anyway, it's not actually
that much more. And if you have gun or battery issues, they'll just fling another one at you and you can get on with playing.
As
@rocketdogbertsays, it's best to ask the local site for clarification on all of this, as their explanations can be a little... minimalst.
And yes, it's fine to rock up solo, we're all there for the same thing, and it's super easy to get talking to people. Just ask someone about their gun, and see if you can get them to shut up.