Do it yourself. Ask lots of questions.
Figure out your pay, probation period, vacation time, benefits, ask if they have an employee manual, etc.
Then, email them, state that you've already started working for them, summarize what they've told you, throw in a couple of assumptions about paid vacation time/sick leave, the starting dates of your benefits, etc.
And ask them to confirm your summary. Either they'll confirm it, or they won't. But either option will be better than you just waiting on them to see what they give you.