مشورت کردن

No, for a dictionary or book, use 'moraje'e kardan' (referring to). 'Mashvarat' is for people.

'Mashvarat' is the act of consulting. 'Moshavere' is the field of counseling or a specific session.

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

There isn't a direct opposite verb, but 'khod-rayi' (self-opinionatedness) is the conceptual opposite.

Yes, it means 'to get advice'. It's very common.

A consultant is a 'Moshaver' (مشاور).

Yes, it is widely understood and used in both Tajikistan and Afghanistan.

Yes, though 'ham-fekri' is more specific for brainstorming.

Not necessarily, but it implies you are seriously considering it.

Yes, couples 'mashvarat' about their future all the time.

Yes, clearly, unless it's very fast informal speech.

It's rare, but you can say it to mean 'deliberating with oneself'.