Hi Tomáš,
You may use AdGroupService with filtering campaignId or campaignName to get specific adGroups. As for getting the Ad information, you will need to make a separate request using the AdGroupAdService. You may then use the following to get URLs of the ads.
You may also use Ad Performance Report as it is possible to retrieve the similar information with the above by filtering CampaignId or CampaignName.
With regard to pausing adGroups, it is possible to use AdGroupAdService.mutate and update the status to PAUSED. You may also refer to this sample for updating adGroups.
Please let me know if you have further concerns.
Regards,
Hiroyuki
Google Ads API Team