Getting and serializing the state of dynamically created python instances to a relational model
Just use an ORM. This is what they are for. 
What you are proposing to do is create your own half-assed ORM on your own time. Save your time for your own code that does things, and use the effort other people put for free into solving this problem for you.
Note that all class creation in python is "dynamic" - this is not an issue, for, well, anything at all. In fact, if you are assembling classes programmatically, it is probably slightly easier with an ORM, because they provide reifications of fields.
In the worst case, if you really do need to store your objects in a fake nosql-type schema, you will still only have to write your own backend driver if you use an existing ORM, rather than coding the whole stack yourself. (As it happens, you're not the first person to face this - solutions exist. Goole "python orm store dynamically created models" and "sqlalchemy store dynamically created models")
Candidates include:

Django ORM
SQLAlchemy
Some others you can find by googling "Python ORM".
I'm developing a framework of sorts. I'm providing a base class, that will be subclassed by other developers to add behavior to the system. The instances of those classes will have attributes that my framework doesn't necessarily expect, except by inspecting those instances' __dict__.  To make things even more interesting, some of those classes can be created dynamically, at any time.
I'd like some things to be handled by the framework, namely, I will need to persist those instances, display their attribute values to the user, and let her search/filter instances using those values. 
I have to use a relational database. I know there are some decent python OO database out there, but unfortunately they're not an option in this case. 
I'm not looking for a full-blown ORM too...  and it may not even be an option, given that some of the classes can be created dynamically.
So, my question is, what state of a python instance do I need to serialize to ensure that I can deserialize it later on? Is it enough to look at __dict__, or are there other private attributes that I should be using?
Pickling the instances is not enough, because I'll need to unpickle them to search/filter the attribute values, and I'm afraid it's too much data to do it in-memory (instead of letting the database do it).