MySQL Master/Slave. Actual use of Slave Machine
Can I simply point my office web server to the Slave MySQL server? Will they be able to write to the slave?


Short answer: Yes, but they probably shouldn't.

Depending on how your application works, it is possible (even likely) that writing to the slave will break replication. Even if it doesn't, over time it's likely that your databases will develop split brain - for example, someone could change some data on your slave that remains undetected for a long period of time.

If you are able to maintain two MySQL servers in your office, I would suggest the following:


Master server #1 on your trailer
Replicant server #2 in your office, acting as slave to #1
"Working" server #3 in your office


Server #3 would be the server that your staff connect to. Set up a job - maybe one that runs each night - which takes a backup of server #2 and then restores it over the top of server #3. This way staff can work with fairly recent data without the risk of affecting replication.

You could even make server #3 a slave to server #2 if it looked like that might work, though I suspect this might cause more problems than it solves. 

Public cell and wifi networks are unlikely to be as secure as you like - I'm assuming that you will secure the connection to your office via VPN. If not, MySQL can secure communications via SSL and you may want to consider that.