Plugin doesn't run on wp-cron

I am sorry, but I don’t really understand what are you asking.

What methods? Plugin does not have any methods hooked to wp-cron.php

Plugin schedules it’s jobs to WP Cron, but it does not interact with it directly.

I mean this: if I will add new post as scheduled, when it publishes, plugin doesn’t share my posts to social networks. that’s it. but on test site, and local site it sends the post to social networks. on live site not send. where would be the problem? but if I publish immidiately plugin shares my posts automatically and immidiately.

Please check your Log/History tab and let me know what do you have there.

Do you have WP Cron setup correctly?
https://www.nextscripts.com/tutorials/wp-cron-scheduling-tasks-in-wordpress/

it writes on this logs:

[2016-03-16 09:14:01] – [Debug info only. – Cron Time] [X] –
[2016-03-16 09:01:01] – [Debug info only. – Cron Time] [X] –
[2016-03-16 08:48:02] – [Debug info only. – Cron Time] [X] –
[2016-03-16 08:29:01] – [Debug info only. – Cron Time] [X] –
[2016-03-16 08:25:04] – [Debug info only. – Cron Time] [X] –
[2016-03-16 08:23:03] – [Debug info only. – Cron Time] [X] –

this is only on that time when I would have scheduled posts, but if I would publish without cron it writes like this logs:

[2016-03-16 09:18:04] – [Start =- ]- ——=========#### NEW AUTO-POST REQUEST PostID:(309919) Immediate ####=========——
[2016-03-16 09:18:04] – [*** ID: 309919, Type: post]- Status Changed: draft_to_publish. Autopost requested.

… . . ..

and that’s why I thought that the plugin doesn’t load on wp-cron running

You have “Immediately” set in the settings. Have you tried to switch from “Immediately” to “Scheduled” in the Plugin Settings->How to make auto-posts?

Also your WP Cron is not correctly setup.

[2016-03-16 08:48:02] – [Debug info only. – Cron Time] [X] –
[2016-03-16 08:29:01] – [Debug info only. – Cron Time] [X] –

That’s a 30 minutes gap between executions. Not ok.