For the first part of your question, your dates are correct - you can apply up to 28 days before 7th Sept up to 5th Oct.
For the second part, yes the financial, accommodation and relationship requirements are the same.
You do need to pass the Life in the U.K. test though.
For the correspondence, I’m not sure - the FLR(M) is 2 years of correspondence but I think it may be 2.5 years for ILR as it doesn’t specify the 2 years, just ‘since last leave to remain’. A couple of people have applied recently so hopefully they can clarify.
For the third part, that’s correct - you need the BRP before travelling. If applying in person the BRP usually arrives within about 4 days but it can take 10 days.
For number 4 - not sure about waiting times but I don’t think it’s too long.
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