If you are in
Revit 2019, please download the
DynamoInstall2.0.3.exe stable build! https://dynamobuilds.com/
As you noted in your original post, best practise is to also uninstall previous versions.
If you install Revit 2020, you’ll get
Dynamo 2.1 and if you get Revit 2020.1 you’ll get
It depends on what version of Dynamo you use - there are breaking changes between the 1.3.4 and 2.0 versions of Dynamo. However, you should be able to use Dynamo 2.1 graphs in Dynamo 2.0.3 as the file format is consistent.
Future functionality (i.e things released in Dynamo 2.1) will not be available in Dynamo 2.0.3, but if the functionality is the same, as most nodal functionality is, then it will work