Ah! If I'm not mistaken, you are talking about form filling. Yes, Bluebeam is not focused much on the form features. But it can do forms in some capacity now. Actually, a few versions ago, it was something I personally requested from them. So now, forms are supported. It's probably not as fully developed as in Acrobat Pro, but it can do it. At least you can fill out pdf form documents and save them (I know you can't save them in Acrobat Reader).
But you should be able to do a,b, and c with Bluebeam. if not, there must be some compatibility issues somewhere. Here's is something I found in the Bluebeam help file, i don't know if it helps:
FDF (Forms Data Format) may be imported and exported from within Revu. This is a format that enables the exporting and importing of data that is entered in the form field.
At this time only Acroform PDFs are supported, XFA forms may not be filled out within Revu.
The other thing that I probably consider a markup, but I don't know if you do, is the typewriter feature that is common to Acrobat. I use that a lot when I have to fill out forms, but the forms haven't been formally formatted in Acrobat (meaning, the places where you have to fill out aren't actual fields). So in those cases, I use the typewriter feature to just point to an area and type quickly. The difference between that and the regular text markup is that the regular one has all sorts of options for font, style, color, background, opacity, fill, etc. But again, I would call the typewriter a markup, to distinguish it from actual saved forms text.