I cannot not send and receive e-mails

Question

Translated with the help of Google Translate.
Mail: Version 7.3 (1878.6)
Two-step verification set
Since a number of weeks I cannot not send and receive e-mails.
And I cannot find an answer in the support community.
I suppose the cause can be found in the two-step verification or in the TLS certificate ... but in this I am a layman.
The connection wizard explanes:
iCloud IMAP Failed to log on this iCloud IMAP account. Make sure the username and password are correct
SMTP Failed to log on this SMTP account. Make sure the username and password are correct.
I'm 99.999% sure that the username and password are correct. Those missing 0.001% can be found in another problem somewhere else. Who advises me?
My settings are as follows:
[Account Information]
iCloud IMAP
E-mail: [email address] @ me.com
Incoming mail server: imap.mail.me.com
username: [email address] @ me.com
password: my iCloud account {four digits, a hyphen, five Uppercase, 1 lowercase}
server name outgoing e-mail: smtp.mail.me.com
TLS certificate
[Outgoing mail server / Edit SMTP Server List / account information]
Server Name: smtp.mail.me.com
TLS certificate
[Outgoing mail server / Edit SMTP Server List / advanced]
custom port: 587
Use SSL: yes
Authentication: Password
username: [email address] @ me.com
password: that of my iCloud account
[Advanced]
IMAP path prefix: left blank
Port: 993
Use SSL: yes
Authentication: Password
Use IDLE command: checked.
I hope I get soon an answer.
iMac (27-inch Mid 2010), OS X Mavericks (10.9.5), Mail

Answer 1

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What does Mail/Window/Connection Doctor Show? If the server is red, select it and look at the Show Details box.
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