Alexg has got it right, in my view. However, since OP says he is waiting for someone to provide a generalized answer, here's mine.
It is hardly ever wrong to omit the article. "The Mall" is the name on the signs, so must be used: "Strand" (the formal name) is both awkward and confusing, so 'the Strand' is usual: most English towns have a few similar names.
Otherwise, there are many names that have developed from descriptions; 'London Road' is the classic example. Most towns in the Home Counties have a road that leads towards London, and refer to it as 'the London road'. Often, when street names were being given, it was named "London Road". In such a case, locals will often call it 'the London Road', while outsiders including the Post Office call it 'London Road'; I wouldn't say either was right or wrong. (Road is, in practice, the only term to which this applies: "the High Street" is usual, but so is "Church Lane is the high street in that village.")
Similar rules apply to stations, airports, roundabouts, etc. Bournemouth has a roundabout with a Frizzell office block, which everyone calls "the Frizzell roundabout". The council put up a sign saying "Frizzell Roundabout", so you can call it either. As far as I can see, all names with articles follow this rule: you can call what used to be Eastleigh Airport (the airport for Southampton) either "Southampton Airport" or "the Southampton airport". "The Southampton Airport" is not correct, but is an understandable mistake; if enough people use it, the name will change.
One last purely national point; in theory, you could refer to a railway terminus named 'Thingtown Central' as either "Central Station" or "the Central"; maybe this happens in the US. Britain has too many places like Exeter, where Exeter Central is a suburban halt, and the central station is Exeter St David's. (The explanation is historical.) So "the Central Station" would be highly ambiguous, and is never used.
You have an (or a) average, maximum, minimum, or other group-based calculation of something, while you take (or calculate) the average, maximum, or minimum.
Thus your samples 1, 3, and 5 are correct, but not 2, 4, or 6.
(To clarify, as per the comments: In the example sentences, the average is a property that is already known, and it is being treated grammatically in the same way as a generic, indefinite possession and thus can take the indefinite article 'a'. If the average is an unknown number that needs to be determined, then you are taking or calculating it, and then it is a specific feature and should be referred to with the definite article 'the'.)
Best Answer
For dates, there is a difference between British and American English.
"April first" is fine in (spoken) American English, but is uncommon in British English, where is would either be "the first of April" or "April the first".
Incidentally, the different word order here may reflect the fact that Americans tend to write dates with the month first, so for example, 1/31 or Jan 31, compared to British 31/1 or 31 Jan.
Regarding the other example given, it could be argued that the word "its" has been omitted, i.e. "Setup is preparing your computer for its first use"; "the" in this case would imply that it's something else that is being used for the first time, e.g. "Setup is preparing your computer for the first use of the new printer".