1. When you Publish pages on the Source Variation it copies that page content to all the Target Variations (labels) as a new minor version of the publishing  page.
2. Because it's just a minor version of the page that's been created in the Target Variation, the local admin for that variation can refuse to Approve the version. They therefore have control over what is published to the general readership on their variation.
3. If the English site makes changes and publishes a new version then that will get pushed down to the Target Variations as before. Any translations they've made don't get overwritten (because they'll have saved their translations to yet another minor version of the page) but a new minor version in English will get created in their variations. It's then up to the local team to merge any small changes into a new translated copy. The important thing to manage here is that changes aren't published from the Source Variation too often because of the work this causes in translation (and perhaps localisation) for the guys managing the Target Variations. Ideally, the English site won't be publishing major versions of pages and then making a minor change and publishing again too quickly.

Some of how you manage this depends on your translators. If they are an external organisation for instance and there's some lag (and cost) to each translation then perhaps you might smooth the process by getting new copy translated once a month (if this meets business needs). The reason I'm suggesting this is if the Source Variation doesn't have the discipline and keep publishing out relatively minor changes, a lag between kicking off your translation and localisation processes might save you considerable costs by rolling several versions of change into one translation exercise.

You'll notice I keep mentioning localisation as well as translation. Don't forget that business material may not be applicable to other countries by just being translated. There may be legal differences between the countries, or other constraints on the business which mean you also need your business people to localise any copy you push out with variations.

I've said it before and I'll say it now; Variations are trying to solve a difficult business problem, and can't possibly provide a full end to end solution with current technology. Manual steps will always be needed, or hefty custom development to suit your circumstances. You need to think through carefully how you will manage your multi-lingual web content whether you use variations to achieve it or not.