I personally wouldn't trust information on that website any more than I would trust information on a pro-academy site. Both sides are prone to twist facts.
Am I right in thinking that LAs set rules
No. The LA sets the admission criteria for community and VC schools. VA schools, free schools and academies set their own admission criteria. All types of school must admit a child with a statement of SEN naming the school even if there are no places available. All types of school must put looked after children ahead of other children (although it is a little more complex than that for faith schools). After that it is up to the academy what criteria to use and what order to put them in. They can use the same criteria as the LA or choose their own provided they stick to the rules in the Admission Code (which seriously restricts what they can do).
Who would the dfe send out to the school for 'boots on the ground' so to speak
If funding is being withdrawn because the school is failing (the most likely scenario) that isn't clear. Several academies have gone into special measures and come out again so that process is well known but it is not clear what would happen if the school failed completely. A community school in that situation would usually be closed and the pupils dispersed to other local schools. It may be that the same would happen with an academy but until one gets into that situation I don't think we know for sure.
does 7 years notice mean that two years down the line when they realise it's a financial disaster waiting to happen/ waaaay too much work, they will have to wait a further 7 years notice
Many academies have been open for more than 2 years and none have yet found it a financial disaster or too much work. I can't see any particular reason why it would be a financial disaster - the school receives the same funding per pupil as local community schools plus a bit extra to cover the services that are no longer being provided by the LA (which are much less than most people seem to think - I often see people saying "They won't get X from the LA any more" when in fact they don't get X from the LA now). To answer the question, the academy trust can exit by serving 7 years notice or by passing a resolution winding up the trust. If they do run into serious financial trouble the Secretary of State can terminate the agreement with immediate effect but there are various measures that kick in before that to try to prevent the academy's difficulties becoming terminal (as would also happen if a community school got itself into difficulty).
Where do I actually get indisputable facts about this process
If you are after facts I have yet to find an error of fact on the DfE website. It is, of course, pro-academies so may gloss over some areas or present a positive spin but the facts it states are accurate. Most other websites on both sides of the debate make statements that are simply untrue.