Hi! Welcome to SOFT
I'm quite disappointed that your son is not setting up his own guitar. Like a car lover should polish he own car.
As said in the post above, Mike and Beez are the people you would want to look for for such set-ups.
But, its good to learn how to do it yourself too. The top E string breaking? what is the string gauge that you are using? anything thinner than 0.10 inch is very likely to break with floating bridge abuse.
And please when tuning up the string, do not tune higher then E5 for the 1st string. Its not meant to tune any higher than that.
To get the guitar with a floating bridge in tune, its best to tune up from the lowest string first (Low E), working one string at a time. After tuning all 6 strings, all strings from string 2 onwards should be quite out of tune. Check the 6th string. Lets say its now C3 instead of E3 (2 steps too low), you should tune up and compensate for the rest of the strings by a similar amount, i.e. 2 steps too high. So you should tune the 6th string to G#3. In no time all your strings would be in tune. Its really quite maths based.
After a few times tuning the guitar with a floating bridge, you will get the hang of it. Please enlighten your son with the tuning technique once you think it is the right time.