I was going to stress the importance to you of really knowing the process from beginning to end before you make an offer on a home, but unless you have a time machine you you can't get back to that point, so you are going to have to work with your options from here.
I believe getting a real estate attorney to review the escrow & loan application information won't be a good use of your money. Attorney's are expensive. Instead use another professional you are working with, like your real estate agent as well as non-profit agencies or other inexpensive resources. While real estate agents aren't usually also mortgage loan officers, many of them have some mortgage background or have connections to loan officers. So if needed, they can have the paperwork reviewed by one of their trusted loan officers, and then they can talk to you on the phone about any of your questions & concerns.
When you lock in an interest rate, you will get a Good Faith Estimate which will specify the interest rate and rate lock period/expiration date. http://www.hud.gov/offices/hsg/ramh/res/gfestimate.pdf
is what the Good Faith Estimate looks like. Look at "Important Dates" on page 1. Is there a # of days listed in #3? If so, then your interest rate is locked and that is how many days you have until it expires (from the date of the GFE at the top right of page 1). If it has a "N/A" or something similar, then it is not locked and your interest rate is "floating" with the market.
A lot of lenders will also send a "Rate Lock Disclosure" with more or less a written description if your loans interest rate is locked in or not.
I am a bit confused on what "escrow and bank paperwork" this is. There is a lot of paperwork that goes to the buyer in a purchase transaction here in California. The lender may send you an initial application & disclosures with a "TBD" address on them, then after you get an accepted offer then you'll get an application & disclosures with the exact details of your transaction (address, purchase price, loan amount, etc.). The escrow company will also send you out an initial package called the "Escrow Instructions" along with other paperwork (some of which needs to be completed and sent back). Once your interest rate is locked in, by law you are required to be sent new redisclosures including a good faith estimate with the interest rate, rate lock period, and other details. After your loan has made it through the entire underwriting process, and the lender has cleared your loan to close, and after your rate has been locked, then the lender will send a final set of documents to the escrow company to prepare for the loan signing (in front of a notary). Is that the paperwork? So this paperwork could be those initial loan application & disclosures & escrow instructions, which you'd certainly want to go over, but are not the loan terms set in stone... or it could be the final paperwork you are going to be signing in front of a notary, which would be THE most important paperwork you'll be signing to buy your home. It needs to be clarified, or you'll be getting advice that is all over the map.
Other questions I have...
1. When was your offer accepted?
2. When is your anticipated closing date?
3. Are you qualifying for the CHDAP down payment assistance program? Or are you saying the home that you are purchasing it as a 2nd mortgage from CHDAP on it?
4. Is your 1st mortgage through CalHFA?