Adopting a child in protective custody. ?

Yes, please let the social worker know what happened. It's an important part of the reason why it would be unsafe for her child to return to her.

Now, about the adoption, is this something you want to do? Can you afford the time, energy, and money it takes to raise the child? Because, if you can, it would be so much easier for the child to be adopted by you than to be bounced from foster home to foster home. Let the caseworker know that you're interested, and she can take it from there to figure out whether you're eligible to adopt.

What a sad situation for your friend and her child.

Different questions with different answers:

1. I don't think you need to "inform" the case worker. The mother has already been deemed unfit.  What's happening now doesn't change that.  If the authorities have been called in to search for her, CPS will find out eventually.

2. Whether or not you can get either temporary custody or adopt the child will depend on whether or not you meet the states criteria to either foster or adopt a child. CPS and or an adoption lawyer can tell you want those criteria are.  Usually a social worker will check you out -- this includes a background check, financial review, and talking with your employer and neighbors. 

3. You need to ask whether or not the mother's parental right have -- or will be -- involuntarily terminated or if the mother will have to relinquish those officially. In many states, the goal is to foster a child in the hopes that the parent will get help and become "fit."  Having a child taken away does not automatically mean that the child can be adopted.  

Relatives are the first choice in placements from foster care. There are no relatives and no comparisons of home studies in you post... but they matter. The suicide attempt just confirms that mom shouldn't have custody at the moment.

you should be able to adopt her, someone needs to

Again this is another blame me for what the courts already saw is your fault.