For reference to my answer let me say that I have a 14 year old boy and understand the challenges of being a single parent to a teen.
With that being said -
Dating: 12 year old children should not be allowed to date, either alone or in groups, without appropriate adult supervision. I would never let my boy, at 12, go off with a group of children and no supervision. I don't let him do that at 14.
Respect: Rules must be set in her household - if the boy is disrespectful, there should be consequences that are adhered to at all times. She is the parent and needs to take control of how she is treated in her home.
Chores: At 12 the boy is certainly old enough to contribute to the household chores. At that age mine was doing his own laundry, which he continues to do. He also mops, alternates doing dishes with me, mows the lawn, cleans his room, and takes care of our dogs. I keep a "chore chart" on the fridge for both of us to keep track of our "duties".
Electronics: It does not matter who gave the cell phone, Ipads, stereos, etc. to the boy. They are in her home and she gets to set the rules on usage in her home. Again, she is the parent and should be in control.
Money: She needs to open a 2nd account in both her and her son's name, and have child transfer a percent of that money into savings each week. Again, she is the parent and should be in control. There are set consequences when he does not do his chores - loss of privileges and allowance. Again, she is the parent and should be in control.
Custody: If Dad were serious about a change of custody he would have taken her to court already. He, and the son, are using emotional blackmail to get their way. She needs to let her son know, in clear terms, that she will no longer be swayed by that line of reasoning. My son went through a "I don't want to live with you" phase. Being me, I said fine, call your Father and I will drop you off....you can spend the next school year with him. He backed down very quickly. Sometimes, as much as it hurts, we need to call their bluff.
Our job, as parents, is to lead our children into responsible, successful adult hood. Your friend needs to be the one in charge in her home...right now she has abdicated all of the power to the 12 year old. It is not an easy thing to take back power from a tween - but through consistency it can be done. Help her set up rules and consequences that she will follow through on and support her so she can stick to it.
I feel for her - it is very hard to parent when the other parent is undermining your best efforts. But she needs to break cycle of emotional black mail before her efforts become completely ineffectual and she looses all control over the boy.
Wish her Good Luck from me...I am sending thoughts and prayers her way as I type this.