I would like to set a time limit to the account activation link I send automatically to users after they get registered.

There's no functionality for that.

Another thing I would like to do, but I do not know if this is possible : to delete automatically from database all accounts not activated since 7 days.

You'd need CB Auto Actions for that, but I am strongly against automating deletion of users as one mistake and you've wiped your entire database of users. It's better to just do this manually every now and again or not at all. You can filter users in CB > Users Management using Search Tools to help with this.

How can we install CB Auto Actions?

You will first need to subscribe before you can download it as it is a paid add-on.

Is it limited in time?

Once downloaded you can install it as many time as you like on as many sites as you like for however long you like. You however will no longer receive updates or support for it if your subscription expires.

What should we particularly look at when going from pre-production to production site?

Not sure what you mean. Automating deletion of users is highly dangerous in a production environment as again 1 mistake and your entire database of users is gone. I just flat out don't recommend doing this.

Otherwise, what would you recommend if you had, like us, hundreds of subscribers not confirming their emails everyday (spammers obviously)?

Stop the spammers from ever finishing registration to begin with. You can block a lot of spam by simply using CB AntiSpam and one of its built in Captcha solutions. Your alternative is filter CB > User Management every now and again and delete them if you feel necessary to do so. It will be unlikely you will get 100's per day though.