- "Send and receive e-mail; manage your schedule, contacts, and tasks; and record your activities by using Microsoft Office Outlook."
The punctuation in that sentence is correct. The semicolons separate closely related independent clauses. Also, at least one of the clauses does itself contain commas. Those are two reasons why the semicolons are needed. You can use periods (full stops) there, but the semicolons are perfectly appropriate. If it is appropriate to use And at the beginning of a sentence then it is definitely appropriate there.
If a sentence ends with an abbreviation that uses a period (full stop) then that is the end punctuation for the sentence. Do not use an additional period.