Having won the toss, the captain elected to bat first.
Is correct because the captain cannot elect to bat until (s)he has won the toss. You should place a comma before a conjunction introducing an independent clause.
The Captain may 'want' to bat first, but (s)he can only make that decision after (s)he has won the toss. The other team may win the toss ...
What it means
It means that her patients won't be able to consult with her on Monday and on consecutive days after that (the rest of the week). (You guessed correctly.)
With some adjectives or nouns for a time interval or a specific time, English doesn't require a preposition to make them function adverbially. For example:
Janice returns to work next ...