I think there are sentences when "nice" can be used for "dobry", but not here.
RU: Naszy liudi (jest') dobryje. Verb jest' omitted in Russian except for emphasis
ludzie is a group of people containing at least one male, so dobrzy needs to be used here.
dobre would be used in all other plurals.
Dobrze is an adverb, meaning "well."
So 'kind' is ok but 'nice' is not and the word actually means 'good'. It's confusing enough to learn without throwing in 'well it could be interpereted as this'. Can't we just stick to proper meanings? We can learn all the colloquial uses later.
Well, we have to include the 'side meanings', but 'good' is the main answer and this is what matters.
No. What could that be... maybe "Nasi ludzie są zdrowi" (are healthy)? Or "Nasi ludzie mają się dobrze"...