As with any living thing no system is the most important. All are required to a similar degree.
They eat all of the flies- we would be surrounded by them if frogs weren't here. Frogs play an important role in the food web of wetlands. If frogs disappear from an area, the whole eco system can suffer.
Most frogs have lungs, but their are lungless frogs. They can also breath thru their skin.
Frogs have a stomach and gastrointestinal system like most animals, they simply digest their food like you do. :/
The most important system in the upper and lower body is the Circultory System
Flies are a source of food for frogs.
To get rid of the frogs under the house it is important to have the compound professionally drained to get rid of the frogs. It is however important to note that frogs eat insects such as mosquitoes in the garden.
Frogs need air,food and water
The laws of supply and demand are the most important factors in a free-market system.
Mosquitoes are important because other organisms eat them. Such as spiders, birds, bats, and frogs. With out them the food chain would fail. Yes they sucks but there important to the eco system.
Respritory
yes
Yes.