Een kopje thee.

It is neutral. You can use it with your boss or your best friend.

The diminutive '-je' adds a sense of 'gezelligheid' (coziness) and makes the offer sound more modest and polite.

Generally, no. Most Dutch people drink tea black or with a bit of sugar/honey. Milk in tea is often called 'thee op z'n Engels'.

Pickwick's 'Bosvruchten' (forest fruits) and 'Earl Grey' are staples in every Dutch household.

Yes, but it refers to a large mug and is usually something you drink alone at your desk, not something you offer a guest.

It is a 'de-word' (feminine/masculine), but 'kopje' is a 'het-word'. Since 'kopje' is the head of the phrase, the whole phrase behaves like a neuter noun.

It's a verb that means to spend a long time drinking tea and chatting, usually associated with older women or cozy afternoons.

You can say: 'Met suiker, alstublieft.'

Ask for 'een potje thee'. This is common in cafes for longer social sessions.

Coffee is slightly more popular, especially in the mornings, but tea is the dominant drink for afternoon and evening social visits.

It's a slang term for a cup of coffee, but sometimes used metaphorically for any warm, comforting drink.

Yes, it's polite to finish your cup, but you don't have to accept a second one if offered.

It's a bit too informal/cute for a waiter. Stick to 'een kopje thee'.

It's a borrowed British concept, usually a fancy afternoon event with sandwiches and cakes, often booked for birthdays or showers.