Is it possible to provide a summary at the end of a survey showing the participant's responses?
Is it possible to email a participant a summary of their survey responses to an email address they provide within the survey?

I'm on version Version 2.58.0+170104 (yes, I know it's old, we're supposed to update this year)

Yes, you can use the admin notification emails for this ( www.limesurvey.org/manual/Notifications_..._notifications_email ). The field for the email address can make use of Expression manager, so you can pipe the email given in a question into this field, e.g. {questioncode} and then let the respondent receive the notification email.

Adapt the template of the basic or detailed admin notification accordingly (depending which one you'll use for the respondents. You can pipe all answers of this respective participants into the email (but not those of others!).

This is also available in 2.58. If it works as expected is another story, because the version is old and bugs contained in this version might have been solved long ago.