Starting point is that you have one month to request a statement of reasons (a detailed reasoning of the decision by the judge) and a record of proceedings (handwritten notes done by the judge on the day of the hearing.
You can't appeal a first tier tribunal to the upper truibunal on the facts. You have to identify one of the five errors of law and apply for leave to appeal. This is not difficult. Almost all tribunal decision contain an error of law. Most contain more than one. It's near impossible to avoid but you will need expert advice to identify them in the first place.
"A decision based on incorrect assumptions" sounds like you're disputing the facts not the law. However, it could also be an error of law e.g. insufficient findings of fact. Bottom line is to request the SoR and RoP and get advice.
You then apply for leave (permission) to appeal by showing which errors you think apply. This goes to your local HMCTS office. If they grant leave then it gets referred to London. If not then you get one month to apply direct to London.
if the UT refer back to the FTT for a new hearing do the facts come into play again.
A set aside is more related to procedural irregularities e.g. missing paperwork, than disputes of fact.
"... my Mike"?
I've been adopted
At this stage you need expert face to face advice to identify an error of law. Do you have just the statement of reasons or do you have the record of proceedings too? If you don't have the latter then you need to request it quickly.
Impossible to say on here which errors might apply without having sight of the decision, ROP and the appeal papers. Thus, you need face to face advice.
What I can say, as previously, is that much of what you describe above still seems to be factual disputes i.e. over what is or isn't a fact. At this stage that is done and gone. You only get to dispute findings of fact again if you can show an error of law at this stage.
Nope. There should be a ROP regardless in theory.
Maybe post up a small list of your main objections to the decision with lots of specifics? That may enable more informed comment on whether there's an error of law there.