I wasn't expecting all the 39057 warning on here but at least few ...
The RPD can probably be able to produce tons of different warning messages, so if you don't post at least the most frequent one it's difficult to tell you what does it means and what you can do.
Warnings doesn't always means to change structure, most of the time adapting things in the BMM layer is enough to fix them.
The point about "dummy" columns is that every single physical table source used in any LTS need to have at least a mapped column in the BMM (just the BMM, no need to expose it in the subject area. So an easy way to fix is just to add a logical column to your logical tables (facts and/or dims) using a random column of the unused physical source and that fix the warning.
For your analysis not working anymore because of the "no fact table exists" you can maybe check if content levels are correct, sometimes defining the implicit fact column also help OBIEE in case you don't have facts in your analysis and OBIEE has multiple way of answering your query. To make it short: no easy answer to that one ... look at what you are asking to your BI server, check in your model that there is a way to answer that query and that everything is setup in a way that the system can't take a wrong route when trying to join your tables (if you have multiple LTS also check priority groups to maybe force one to be used first than another)