Long vacations are one of the perks of working in this company.

A company car and your own office are only some of the perks that come with this job.

Being able to touch type for programmers is a massive advantage, as you can implement your ideas faster. Plus, you can use your keyboard in the darkness.

Some Soviet political institutions were still in place after the break-up of the Soviet Union up until 1993.

Technically, after the collapse of the Soviet Union, Russia was still living under the Brezhnev's 1977 constitution up until 1993.

They were counting on the faceless bureaucrat they'd put into position to carry out all of their wishes, but it blew up in their faces. The man turned out to have his own opinion on their business and after some time refused to do what he'd been told.

The sale of the house fell through because the owner got offered a better price.

The police are in cahoots with draft boards/(military (is it necessary here?)) recruitment offices over tracking down draftees. They also hit the streets (maybe some other phrase here is more appropriate?) in search for people of military age.

The government and local tech companies are in cahoots over mass propaganda and news manipulation.

He's clearly at odds with the school administration.

His pessimistic outlook on life is quite at odds with his wife's outgoing personality.

The allied parties are at odds over the campaign for the upcoming elections.

I seldom find myself at odds with your insights.

This law is at odds with the constitution.

As a side note, I think it would be good to return/come back(both are fine?) to these phrases at some point to make new sentences to reinforce my memory.