We have a page on mosquito control which likely has information you have already researched, though there are also a number of links to other institutions with further information: https://extension.umd.edu/hgic/topics/controlling-mosquitoes

Encouraging local populations of various mosquito predators can certainly help manage their numbers without spray treatments. The most effective predators will be those feeding on larvae in the water (so, mosquito fish and, as you mention, dragonfly/damselfly larvae), since aerial predators are few. (Neither Bats nor Purple Martins eat a large enough amount of adults to be effective controls.) Gardens or natural areas with a diverse array of (preferably) native plants will keep the insect population itself diverse and supported, which will help feed the adult dragonflies and the rest of the food web. For instance, floral predators like ambush bugs and crab spiders may consume male and unmated female mosquitoes, which visit flowers to acquire nectar to feed themselves.

Dragonflies would also appreciate a water source. If a backyard pond sounds too daunting or you don't have the space for it, there are so many small container water features you could turn into a fun project! Solar fountains come in a range of sizes and various costs, you could even scour your local social media garage sale pages to see if any one is passing something on!

If you search the internet there are a variety of webpages that will list the top 5 plants or top 5 ways to help encourage dragonflies. You can cross reference the list with the species on https://www.marylandbiodiversity.com/ and make sure the plant is suitable for Maryland.

For frogs and toad you would also most likely need a water source to encourage them. They also do well with leaf litter so if you can leave the leaves in garden spaces that will be encouraging. We don't have any bats in Maryland that pollinate flowers but in terms of attracting night time pollinators like moths to attract more bats, that could be helpful. Bat houses need to be a ways up on a tree or a post so there shouldn't be an issue with cats getting close to them in regards to your pets. If you are worried about rabies, that isn't really related since pets should have vaccines for that. Its unlikely that bats would go after any of your pets or bite them.

Let us know if you have further questions.

Emily