Hi @tommypepsi ,
As to your first question: it is not something to worry about too much; you can easily change your mind and make everything one Object (in Object Mode select the different parts that you want to combine and then use the CTRL+J hotkey), or split parts off (in Edit Mode select a part and then use P > Separate > Selection).
With the wheels, if you make them separate Objects, you can indeed make Linked Duplicates, which is an advantage. Also you can have different Modifiers on them if parts are not one Object. (There are some Modifiers that can work on only a part of the Mesh, but not all Modifiers have that ability…)
Basically, just do what you think is best and adapt if necessary.
And for your second question:
intersecting Meshes are extremely ugly and frowned upon and should (usually) be avoided, but with your example, I think you can get away with it (if it won’t keep you awake at night, that is…), because it probably will not be seen and it’s not worth the trouble (just don’t tell anybody…).