What are the minimum requirements to have DB start.
I've finished all of the other DLCs (Hearthfire, Dawnguard)
Having finished the other DLC, my character is at crazy-level 50+.
I was hoping to start DB with a lower level character for a little more challenge.

Here's the questions:

Is there a min. character level?

Do you have to have finished the mq in Skyrim?

I think the min requirement is you have to have finished the MQ where you visit the Greybeards at High Hrothgar for the very first time. This is the quest right after Dragon Rising, where you kill the dragon at the tower located just south of Whiterun, which is when the Greybeards summon you calling "DOVAHKIIN" from the Throat of the World....

Uhh, anyway that's when it triggered for me. I came down from High Hrothgar and was greeted by some cultists in the middle of Ivarstead.

I'm not aware of any minimum character level, you can probably find the ship to Solstheim at level one and go there.

To start the main quest of Dragonborn you need to have completed the Horn of Jurgen Windcaller quest in Skyrim's MQ.