All good answers.
My 2 cents blah blah, far from enlightened but if I had to guess ---
-How is someone's mind after enlightenment?
This question would not arise because there is no reference point of a self having (or not having) anything, including a mind or enlightenment: like trying to write on air or water.
-Is it bliss or joy that enlightenment brings or just silent peace?
Bliss, joy and silent peace would be seen as being exactly of the same nature / quality, as would any other experience, as well. Experiences arise as a display of energy but there is no attachment / clinging or aversion / fear of what arises or doesn't arise. All appearances are of exactly the same nature. This is sometimes called the "All Good" or "same taste", or "one taste" A Buddha would never imagine or speak of bliss, joy or silent peace, though from the outside, these qualities may be imputed to a Buddha.
-Do they still have feelings?
Feelings can arise as a natural display of energy but there is no attachment / clinging, or aversion / fear of what arises or doesn't arise. There is no identification with someone holding / having a thought or feeling. The feeling or thought is experienced and released at the same time - like a snake untying its own knot, a soap bubble bursting or a snowflake falling on a hot stove.
-Do they still have ambitions?
A thought could arise that we would normally call an ambition, but there would be no attachment / clinging, or aversion / fear of what arises or doesn't arise. A Buddha does not come under the power of thought or emotion. Except for the cause of compassionate activity there is no need to do, or not do, anything, including remaining, which is why disciples write long life prayers for the Masters to stay and teach.
-Do they still appreciate worldly beauty such as art or maybe nature?
Thoughts and feelings that we would normally call appreciation of art or nature (including intimacy) may arise but with no attachment / clinging, or aversion / fear of what arises or doesn't arise.
-If someone have a wife or husband or partner, will they lose all interest after enlightenment and abandon them?
Many enlightened Masters, in many ancient and modern Buddhist traditions, have wives, husbands and partners, who are treated with sincere respect and tender love.
-Do they feel pain anymore, say maybe from the lost of a family member or someone close such as a great friend that he or she grew up with and been around their whole life?
Marpa, an enlightened Master, was said to have cried, when his son was thrown from a horse and died.
Thoughts and emotions may arise but without being the cause of attachment or aversion. Perhaps Marpa suffered illusory tears for his illusory son having suffered illusory death.
I would imagine that enlightenment has nothing to say about anything, but shines on brightly - none the less, and so many things may be said (without attachment or aversion).
So to answer the OP's question, "yes", but a Buddha would never think, feel or say this.
I'm just babbling back what I have heard about such things, so perhaps it might be more useful to put these questions to an enlightened Master.
Hope this helps.