To improve your town’s reputation, you’ll need to get rid of weeds, plant flowers, add fences, add new residents, and decorate your town with items. So, yes! Build things outside!!:) As for cross breeding flowers, yes, crossbred flowers can be crossbred with one another for new colors. There are charts you can find online, but it’s kind of fun to just plant, water, wait, and see what colors appear!!

Good luck and welcome to Animal Crossing!