It is a good idea to at least consult with an attorney on an hourly basis even if you decide to handle the divorce without an attorney. Most experienced divorce attorneys try to be a little more sensitive that those on LA Law and will do their best to be good listeners and advisors. At least 4 months, longer if your case is complicated. There is a mandatory 90 day waiting period after the divorce papers are filed, before you can get a final divorce. Most offices can start the process the same day you hire the lawyer.
Lawyers generally charge by the hour.
Usually within 3 weeks of the initiation of the case but you have to request what you need through a Motion. I'll discuss this more fully below. Child Support is governed by the Connecticut Guidelines for Child Support. The clerk's office at your local courthouse can give you a copy of this law which contains a chart indicating how much support is owed for each income level. Your lawyer can also give you a copy of the law.