1. If you say "she is on my work permit", then yes she is in the UK as your dependent. The current visa in her passport states her status, so do check.
2. You may include your wife in your settlement application (
196D).
3. Application form
SET(O), in which you can add her as your dependent applying for settlement at the same time as you.
4. If applying in person at a PEO, you must include your spouse as "additional family member".
5. After you are granted settlement, register your UK born child as British citizen under
section 1(3) using form
MN1. Registration under section 1(3) is by entitlement (no UKBA discretion involved).
6. There is no need to include the child in your settlement application.
regards