Generally, you can use whatever naming practice you want to if you're working on your own. If you're cooperating with someone, it's obviously best to agree on some common standard, but that's between you and the others working on the project and nobody from the outside has any business or right to tell you what is the "right" or "wrong" way to name places.
This also applies to the decision if you want to use the current political structure or the place hierarchy at the time of the event. Decide on one approach, document it if you're working with a team, and stick to it. Both have their strength and weaknesses, so it's best to use them both in parallel where possible, but this is seldom the case. The GEDCOM data format for example doesn't have any capability of recording place hierarchy changes over time since places aren't top-level elements of it.
In the specific case of the USA, I'd keep the "County" part to distinguish place names like these from each other:
- Overlea, Baltimore, Maryland, USA (neighbourhood in the independent city of Baltimore)
- Overlea, Baltimore County, Maryland, USA (unincorporated community and census-designated place in Baltimore County)
This also answers your second question: There are indeed places in the USA where counties do not exist. In particular, Washington, D.C. is not even part of any state and there are 41 independent cities which don't belong to any county.
On the other hand, there are "cities" or metropolises which are spread across multiple counties; you'll have to keep that in mind as well with whatever hierarchy you'll end up using. One example would be New York City, consisting of:
- Bronx County, New York, USA
- Kings County, New York, USA (Brooklyn)
- New York County, New York, USA (Manhattan)
- Queens County, New York, USA
- Richmond County, New York, USA (Staten Island)
There are also places which politically belong to one county, while geographically being split between multiple of them. One example is Bothell, Kings County, Washington, USA which is geographically nearly halfway in Sonomish County, Washington, USA (designated in red in the picture).
