Hello Rémy,
here are answers:
1. To be honest, it is not at the plan yet.
2. First time you have to mark all cat. manually. M-Turbo has a settings that every new cat. will be marked/selected automatically.
3. Cache is refreshed if content is changed. If you change product price, cache for product will be updated. If no change with products for 5 days, cache will be not updated for 5 days as well.
4. You may run from php same script, which is used by cron for automatic update. If you call also magento "update method" for categ/product, cache will be updated as well because content have been probably changed.