E-mail encryption

1) Yes

Encryption occurs in transit and at rest automatically:

https://support.office.com/en-ie/article/encryption-in-office-365-0a322724-08ca-43db-b69a-afbfa20484cd

2) Yes, in as much as emails are transmitted over an encrypted connection:

"Exchange Online servers always encrypt connections to other Exchange Online servers in our datacenters with TLS 1.2. When you send mail to a recipient that is within your Office 365 organization, that email is automatically sent over a connection that is encrypted using TLS. Also, all email that you send to other Office 365 customers is sent over connections that are encrypted using TLS and are secured using Forward Secrecy."

https://support.office.com/en-us/article/how-exchange-online-uses-tls-to-secure-email-connections-in-office-365-4cde0cda-3430-4dc0-b489-f2c0736c929f

3) No, but there are options available such as Office 365 Message Encryption (OME) that can do just that, which

"lets you send encrypted email to people inside or outside your organization, regardless of the destination email address (Gmail, Yahoo! Mail, Outlook.com, etc.)."

https://support.office.com/en-us/article/email-encryption-in-office-365-c0d87cbe-6d65-4c03-88ad-5216ea5564e8