Exim and external SMTP server, how to make mail go?

Question

Debian

Hello dear! Help with wise advice, but with a kind word.
There is a Debian machine behind the router, Apache is running on it with my local web developments. The IP is dynamic, but there is a service on the router that assigns an address like blabla.asuscomm.com
I want sendmail to still send real letters to my mail, for certain tests.
I set exim configured by default only to send. For a while it worked, although it ended up in spam. Then Google banned the IP address.
I decided to set up sending mail via external SMTP, I chose Google.
In update-exim4.conf.conf settings:

dc_eximconfig_configtype='smarthost'
dc_other_hostnames='admin.site'
dc_smarthost='smtp.gmail.com::587

'
The rest is default.
In passwd.client

gmail-smtp.l.google.com:[email protected]:XXXXXXX
*.google.com:[email protected]:XXXXXXX
smtp.gmail.com:[email protected]:XXXXXXXXXXX

xxxxx, respectively, from the box logins and passwords. The rest is default.
The box is working. Checked.
At the first attempt to send mail, a letter from Google fell into the Google mailbox that some application was trying to gain unauthorized access, changed the account settings so that all applications could access Google.
As a result, the mail does not go!
Provider Beeline / Corbina, in the settings in the Personal Account - firewalls are turned off for me, there are no filters. The ports are all open.
Lets telnet:

[email protected]:/etc/exim4# telnet alt1.gmail-smtp-in.l.google.com 25
Trying 64.233.168.27...
Connected to alt1.gmail-smtp-in.l.google.com.
Escape character is '^]'.
quit
221 2.0.0 closing connection p8si4839932obx.27 - gsmtp
Connection closed by foreign host.

In the logs:

2014-10-29 19:22:58 1XjV3L-0007hr-Ow == [email protected] R=smarthost T=remote_smtp_smarthost defer (110): Connection timed out
2014-10-29 19:30:01 1XjVCD-0007pb-Ef <= [email protected] U=adept P=local S=588
2014-10-29 19:30:01 1XjVCD-0007pb-Ef == [email protected] R=smarthost T=remote_smtp_smarthost defer (-53): retry time not reached for any host
2014-10-29 19:32:57 1XjVF2-0007qc-V7 <= [email protected] U=root P=local S=361
2014-10-29 19:32:57 1XjVF2-0007qc-V7 == [email protected] R=smarthost T=remote_smtp_smarthost defer (-53): retry time not reached for any host
2014-10-29 19:36:30 1XjVIU-0007wJ-9y <= [email protected] U=root P=local S=361
2014-10-29 19:36:30 1XjVIU-0007wJ-9y == [email protected] R=smarthost T=remote_smtp_smarthost defer (-53): retry time not reached for any host

Who is to blame and what to do? Google? Provider? Router? Exim change to something more digestible? Exim is not set up like that?
Wasted a lot of time on all of this...

Answer 1

Google has worked. Apparently there was a ban with SP - when the security settings were not configured yet.

Answer 2

It’s possible and much easier to move here, just download this small plugin https://wordpress.org/plugins/smtp-mailer-wp/ and there will be no problems at all then, everyone can simply and easily install external mail and you won’t need any hemorrhoids associated with this, so use it to your health and then there will be no problems with this matter, which is not easy, but necessary! I recommend to get acquainted!