It is fine according to the code I work with. Its redundant to have 2 vents on the basement fixture though. Are there other fixtures you are not showing?
yes, but looking closer at your drawing, the first floor sink is draining into a vent or is it mislabeled. If thats the case then I cannot recommend your new vent location. In my neck of the the woods, that is an illegal wet vet. I'm not clear on whats happening on the left side of your drawing. At any rate, it will function as you show it.Verything related is there.
Are you saying I can remove one vent for the sink and connect the red line above the sink drain? Like this drawing?