What happens if it rains on game day? Do you play anyway or does it get cancelled?

It depends on the field and the intensity of the rain. I've been in fields that have cancelled the match due to bad weather and caution, and a week later it was played in the rain because it was only for a while. The best thing you can do is call the field and ask about their policy regarding these situations.

The replica will hold up more or less depending on several factors: if it's gas or HPA, it shouldn't have any problems with its operation; if it's electric and doesn't have good sealing on the electronic part, you could damage something. I've played with my electric one in the rain several times and nothing has happened to it, but if something does happen, I know it will have been my fault for exposing it to the weather. Regardless of this, keep in mind that metal rusts with moisture, so when you're done playing, make sure to dry your replica well as much as you can: use a towel and, if possible, a hairdryer.

When the weather looks bad, you can bring waterproof ponchos; there are also waterproof boots and other waterproof accessories to keep you from getting cold afterwards. Wrap up well and that's about it. Be careful about where you leave your things so that a gust of wind doesn't blow water towards the kit you've left at the base, and be careful about slipping because of the mud.

As for getting your replica wet, I wouldn't advise using a hairdryer at all. Applying external heat to an electrical circuit can break it. The ideal thing would be to disassemble the upper of the replica at home after the match, dry it as much as you can with a cloth and let it dry on its own. If it's a GBB disassemble it completely as it's easier and you can take the opportunity to clean and lubricate it so some parts don't get oxidised.