Can I use existing horizontal tub drain pipe as vent and add new vertical pipe to drain?
Depending on your location, this may not be up to code. Under UPC, a dry vent cannot be horizontal until it is a few inches above the fixture it vents. If your drain pipe backs up over time, you'll have water enter your horizontal vent section, where it can deposit solids and cause the vent to clog. A wet vent can be horizontal because it's expected to be flushed out by other fixtures that drain through it, but there's nothing to stop a horizontal dry vent from becoming clogged over time. Your proposed setup is more likely to suffer from a clogged vent than your current setup.