It depends how you use much. Looking at the first sentence you quoted, it is clear that much qualifies the comparative adverb faster.
She runs much faster than he does.
If you use the simple adverb rather than the comparative, it doesn't work:
She runs much fast -wrong
She runs a lot fast -wrong
She runs very fast OK
If you remove the last half of the sentence so that much qualifies the whole sentence, it doesn't work, but it's OK if you use a lot instead or if you change it to a negative statement:
She runs much - wrong
She runs a lot - OK
She doesn't run much - OK
Looking at the other sentences you quoted:
May we all be having this much fun and getting this much exercise when we're his age!
After much consideration I will NOT be performing at the Inauguration with my improv group
In these examples, much qualifies a non-count noun, not a sentence. That is covered by this page.
Note that, when qualifying a noun, a lot of is more likely to be used than much. unless it follows some other qualifier like this, how, too or very, where one cannot use a lot of.
Let's look at the situation when much qualifies an adjective:
He is much good - wrong
He is a lot good - wrong
He is much better - OK, because better is a comparative adjective
He is very good - OK
He is not much good - OK
He has done much good - OK, because good is a non-count noun in this context
To sum up:
If much qualifies a simple adverb, a simple adjective or the whole sentence, you can use it in a negative sentence but you can't use it in an affirmative sentence- you must use a lot for sentences and very for simple adverbs and simple adjectives.
If it qualifies a comparative adverb or a comparative adjective, you can use it in negative and affirmative sentences.
If it qualifies a non-count noun, you can use it in negative and affirmative sentences, though usage in affirmative sentences is rare unless it is preceded by a further qualifier.