My thoughts on keeping rain out would be to add a roof/umbrella type design on top of the feeder. Nothing fancy, just another pan that is wider.
Here are my designs. The idea is to keep the outlet small. That way, the birds won't scratch or bill the feed out too much. The outlet is also raised off the floor to minimize dirt and droppings from getting into it. I use animal safe sellicone to bond the lip to the bottles. Can find it at Tropical Fish or Pet stores. To cut the openings, I found it easiest to use a soldering iron. With the heated iron, you can just cut/carve easily into the plastic. Height placement and size of outlet is totally up to you depending on what birds it will be used for. I made some for chicks and adults as well. You can just eyeball it by referring to your birds.
You can use plastic juice bottles of various sizes. They are easy to clean and readilly available. Since they are clear, can easily see feed/water level.
For the outlet/lip, I use smaller bottle/containers such as dishwashing soap bottles, shampoo bottles, etc. Cut the bottum portion at the size you desire. Then cut in half. Only need one piece per feeder/waterer.
You may need to trim/shape the outlet/lip if your feeder/waterer bottle is round. Again, you can use a blade or soldering iron.
Cutout for feeder hole. Either use a rectanglar or pyramid shape. I like the pyramid type shape. It helps from feed blockage.
Cutout for waterer hole. Need two holes. Don't put them too close together or water won't dispense. Make sure the seal is good with the sellicone or you will get leakage.
This is the design I use in my wired pen. Helps from waste. Your basic gravity feeder with four openings at bottum of bottle inside of a cd cake case. The case then has four openings that is just big enough for your bird's head to eat from. Use sellicone or anything to bond. Can make similar on a bigger scale.