Re: 1, you can set it in the database as a UTC record and then have it visually change in the HTML (using javascript) with several options.

Eg: If I select 7am on 6/15 from your dropdown list, you render some inline HTML that shows some/all of the following:

"7am EST" "4am PST" "6am CST"

etc

Timezones are definitely tricky, but if you search StackOverflow or other sites there might be some good recommended approaches.