Aleksander, it's good to hear you want to do this with the DGN. As you're aware MX is a 'Powerproduct' so you have all the drafting capabilities of Powerdraft / Microstation.
It's not clear how you exported the model to 2D or where you are seeing 'greyed' out properties. There are however many ways to achieve this in MX, so I'll give a possible workflow but I think some cross training to familiarize with the available tools / processes might be a good idea.
By default MX produces dgn's using the seed file 'mx_seed_m_3d+2d.dgn', this creates a 3D working model (named MX) and a 2D view representation (named 2D MX) that references in the 3D MX working model - ie is suitable for drafting on but you are working on referenced information. This 2D dgn model can then be used for drafting purposes and you have the option here for the refernce of 'Merge into master' which publishes the 3D MX model into the 2D model as native CAD graphics ready for editing. So all normal level / style properties will be available. Personally I would create a new 2D dgn, reference in the MX 3D design model dgn and then do the merge.
Obviously if you are trying to achieve CAD standards then time might be better served if this is a reoccurring thing to setup the PSS to achieve the levels / colours from the get go.
I hope this helps
Regards
Ian