Yes, for both Multiple Choice and Dropdown questions, toggle "Include an "Other" option to specify another answer" in the question configuration.
Can I let the user type in their own answer for a multiple-choice or dropdown question?
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Can I let submitters choose multiple answers for a multiple-choice or dropdown question?
Yes, Multiple Choice and Dropown fields both support multiple answers. You can turn this on by toggling "Can choose more than one answer" in the question's configuration.
How do I add multiple choice questions to my form?
On a blank line, type "/multiple" and select "Multiple Choice" from the popup menu, or click "Add questions" and select "Multiple Choice" from the question dropdown.
Can I limit the number of options that can be chosen for a Dropdown question?
You can allow multiple answers to a Dropdown question, but you can't specify a minimum or maximum number (you can with Multiple Choice).
How do I add a dropdown field to my form?
On a blank line, type "/dropdown" and select "Dropdown" from the popup menu, or click "Add questions" and select "Dropdown" from the question dropdown.