I am looking for privacy screening - if anyone has any other suggestions besides the two trees mentioned let me know :)

Please do not "spray" these shrubs. You are harming birds, bees, butterflies & all kinds of other beneficial insects. The insecticide is far more harmful than whatever "pest" you are trying to eradicate. If you have a plant that regularly becomes infested, it's a sign the plant does not belong in whatever place--or possibly region--it is planted in. Even so-called organic insecticidal soaps kill honey bees & butterflies. There is no such thing as a "safe" garden chemical.

Looks like Ironwood. There are two common types of Hornbeam - this appears to be ostrya virginiana, but check your bark closely ( I can't tell from photo) against google images to know for sure. The other is carpinus caroliana.

It is a spruce and yes you can trim the bottom. We have many and unless it is a dwarf they grow tall and just keep getting wider every year. They also look kind of neat with the bottom taken out IMO