It does matter that you live in Maine as adoption procedures are state-specific. Generally you use service by publication (in a newspaper) if the birth father cannot be found.
As to the bf adopting outside of marriage, a "step-parent adoption" is generally easier than a stranger adoption. Your friend and the bf will need to convince the court that they are offering the child a stable home, which may be easier if they are married. They can call the local social services office and set up an appointment to meet with a social worker who does adoptions and discuss it with him / her, or speak with an attorney who does adoptions. And, regardless whether they are married or not, adoption can set your friend up for a custody battle if she and the bf split up.
There are many services that you can check with such as Catholic Community Services, Comunidades Unidas if you have one in your area or call different law firms although many of the free services tend to give basic advice and assist you with reviewing your forms. They don't fill them out for you normally. I would suggest that you get all of your documents including the foreign passport, birth certificates, birth certificates from children or spouse born here in the US, tax and work records, school records etc... Once you have all of these things together then it will make it easier for the lawyer that is helping you. Normally a good immigration lawyer runs about $250 per hour. Understand that the forms are also expensive, you can fill out financial waivers but they may or may not grant them. Many of the forms cost over $500 to file depending on which ones you need to fill out. It is very important that you do it correctly otherwise your petitions may be denied. Many times they are denied even when filled out properly so you may need to file them again and again. Each case is different so you need someone familiar with immigration law and anyone that will spend enough time on your case to make a difference will normally not be cheap. Many religious organizations can give you referals to lawyers that may help you. Free lawyers also expect you to do much of the footwork so get your paperwork in order and make them a copy, keep a copy and put another copy of all your paperwork at a second location in case you loose your copy or the house burns down. Many of the free lawyers will give you an outline of what forms need to be filled out and you can then print them off from www.uscis.gov use a notebook and take good notes of the order of the forms and on the site the prices will also be listed.