Is there an admission fee - or one to ride the elevator to the top?

Yes there is a fee for the observatory. I went to the restaurant instead and ate, but I did see a group just order a drink and enjoyed the view that way. There's no fee for the restaurant or the bar.

There is a fee to park and just go to the observatory but if you eat at the restaurant or go to the bar no

If you plan on eating at the restaurant or go to the bar then there is no fee.

Yes last all day

Yes