Implement quick translation as primary translation tool in organisation

I don't think that's possible without getting at least one extra floating license. But you should contact your FME sales rep to see what options you might have

You can't buy "only" the Quick Translator, but you can of course hide the other components from the start menu, so that's an option to consider. It would have to be a floating license if it is going to be used on multiple computers and you'd have to make sure your colleagues shut it down after the translation, to avoid blocking a license.

There is a local government subscription available and depending on where on that scale your organisation sits you may want to consider FME Server instead. It actually comes with a generic workspace that pretty much copies the Quick Translator functionality.

As mentioned, you could quite easily restrict your users to Quick Translator only. But to be honest, the better solution here is with FME Server. That way your users can run a translation at any time they want, with no licensing worries, and without having to learn how to use FME at all.

You really should talk to your salesperson to see what is possible. For example, you could use FME Cloud as a hosted FME Server, and you would only pay for it when the machine is running. If that was during business hours it could be as little as $10 per day. Or you could go for a local government subscription where you could pay a set fee for the year and everyone can then use as much FME as they want (including Server).

So I do strongly suggest you talk to your sales representative. They could very well be able to come up with a great solution for you, without costing a fortune.