[a confused chiral girl]

these 2 structures, the second one has a hanging terminal end groups that do not form a second ring.
the first structure, how come it is also aromatic since the F has sp3 configuration, and how do you know one of the lone pairs around the Oxygen atom belongs to p orbital...so it is sp2 instead of sp3??
thank you! 

[Ψ×Ψ]

They're not exactly "aromatic" per se, but they are part of the pi system.  If you have a lone pair adjacent to a p orbital, it goes in a p orbital too.  P orbitals on adjacent atoms do strange and interesting things.  I'm guessing they maybe touched on that in class?  The things going on in the first structure aren't always explained so well.

[Mitch]

What do the molecular orbitals on an SP₂ Nitrogen look like?

[movies]

What do the molecular orbitals on an SP₂ Nitrogen look like?

Surely you mean atomic orbitals!