I come from a python world where only hashable objects may be used as keys to a dictionary. Is there a similar restriction in C#? Can you use custom types as dictionary keys?
The requirement for a dictionary key is that it is comparable and hashable. That's turtles all the way down in .NET, every type (other than pointer types) derives from System.Object and it is always comparable thanks to its Equals() method. And hashable thanks to its GetHashCode() method. So any .NET type automatically can be used as a key.
If you want to use your own type as the key then you only need to do something special if you want to re-define object identity. In other words, if you need the ability for two distinct objects to be equal. You'd then override the Equals() method, typically comparing fields of the object. And then you must also override GetHashCode(), equal objects must generate the same hash code.
If the type cannot be changed or you want to customize the behavior especially for the Dictionary then you can pass a custom IEqualityComparer<> to the constructor. Keep in mind that the quality of the hash code you generate with your own GetHashCode() determines the dictionary efficiency.