Hi Geraldine,
Awesome questions! Here are the answers.
No, Alexa cannot call 911. However, you can say “Alexa, call for help” and reach an emergency contact IF you set this up ahead of time using the Alexa app. Here are the steps

1. Open the Alexa app and tap “Communicate” in the bottom navigation bar
2. Tap the person-shaped button on the top right of the screen
3. Scroll through your list of contacts until you find the person you want, then tap their name
4. Tap “Add as Emergency Contact” 
5. Select which of the contact’s stored numbers you would like Alexa to call and text (Pick a cell phone number to enable both! Your chosen person will get a text message letting them know they were picked)
6. Test it out by saying “Alexa, call for help.” Your emergency contact will receive a text that says “Emergency Alert: (Your name) or someone in their home just called for help. You can call them back on their Echo device from your Alexa app, or try calling their phone,” and their phone should ring with you on the line from your Echo.

Yes, Alexa can call anyone in the country (except 911). There are 2 methods:

• If the person is saved in your phone’s contacts, you can just say “Alexa, call (name of contact)”, and the call will be connected. If you have multiple numbers stored for that contact, Alexa will ask you which one you’d like to call first.
• If you know the number, you can just tell Alexa to dial it by saying something like “Alexa, call 212-555-1212” and the call will be connected.

No, your phone does not have to be turned on for it to work. I just tested it with my phone in Airplane Mode, and it worked without issue.
Hope that helps!!