Do I need to use a period after the abbreviation etc. even when it is followed by a comma?
The abbreviation etc. always ends with a period, regardless of the additional punctuation that may follow. If etc. ends a sentence that takes a period, only one period is used.
In the last example, you may have noticed that etc. is followed by a second period at the end of the sentence. The second period is needed because etc. is within parentheses.
Even though the examples don't cover all of the possibilities, the rule never changes—etc. always takes a period.