Are you suggesting that it is impossible to build a subway where groundwater exists? [1]
All sizable tunnels have ventilation. While we still run combustion engines, we could capture unburnt fuel vapor and use it. With electric vehicles the capacities needed are much lower.
> How do you keep the precious animals you're trying to save from getting in there and getting trapped or run over?
Animals will not have a reason to enter if there is not something to be gained. Currently, they are provoked by the need for water and food, which justify the dangerous risks they must take. Living every day as a gatherer with no guaranteed access to water is not something I'm not convinced you have the empathy to understand.
[1] http://scienceline.org/2010/02/what-would-you-do-with-eight-...
No, merely expensive. The Gotthard Base Tunnel is US$10.3 billion for "a route length of 57 km (35.4 mi) and a total of 151.84 km (94.3 mi) of tunnels, shafts and passages". (Quoting Wikipedia.) That's $290 million/mile.
The Fehmarn Belt Fixed Link is estimate to cost €4.7 billion for 17.6 km of immersed tunnel, or $480 million/mile.
The boondoggle that is the Alaskan Way Viaduct replacement tunnel is in the same range.
By comparison, a rural interstate road costs about $5 million/mile, or a factor of 50 cheaper.
How deeply have you thought this idea through? What happens in places like Florida where the water table is so high you can't dig deeper than a few feet? How do you manage entrances and exits, how do you make sure there's breathable air down there in case people have to get out of their cars? How do you vent poisonous gases? How do you keep the precious animals you're trying to save from getting in there and getting trapped or run over? What about emergency access? You can't open a gate on a service road and suddenly be underground.
Those are just a couple of simple practical considerations that don't even factor in cost, which would be prohibitive.