I feel your pain! I don't have wood slats though. I used to have a woman who would scream bloody murder when me or anyone above me over watered. Rude obscenities. She also reported me to our condo association. Once when sitting quietly outside reading, the person above me overwatered and it dripped directly on me so I politely called up. I got as far as "excuse me to the person above watering..." when the rude lady below me starting yelling threats to call the condo association. When she was done I responded that there was no need to be so rude. She shut up and has since moved. That said, I had old towels lined up by the edge of my balcony and was very careful watering. Plus I watered early in the morning and during the day when I was able to work from home...aka anytime when the nasty lady wasn't out. Have you tried self watering tools? Most decent garden centers have them and Gardeners.com has an assortment--kinds that water when you're on vacation to smaller daily ones. They'll slow release so should help.

Peas and spinach like cool weather, as you have experienced with the bolting spinach. The arugula is probably being eaten by cabbage worms or flea beetles. What kind of soil conditions do you have? A garden that grows well depends on a lot of factor: choice of plants, soil conditions, nutrients in the soil and proper watering.

You have a raised bed so you won't need stones. In fact, having that moisture reserve may be beneficial during hot, dry weather. Mulched soil stays cold longer in spring,so mulch when weather turns warm or hot.

Lettuce and carrots, lettuce especially can be planted within 4-6 in of the edge although it may overlap the edges as it grows. Carrots will work with that same edge spacing but not flush. Solid walls, when the roots of the plant hit them, cause coiling and twisting of the roots so needs to be avoided when possible. Tomato plants at least 8" out from the wall work best IME. Indeterminate varieties, if grown in actual cages rather than those three ring junk things, and if carefully pruned would probably do ok with 4 in a 4x4' space but it will be very crowded, difficult to access for harvest and to monitor for pests. Plus you don't indicate where you live so I can't really address the disease/air circulation issues you might have. Staked and heavily pruned they would do fine in that sapce but the pruning costs you production. Personally I would do 3 tomato plants in that space. You could plant some extra lettuce around it but the plants will shade the lettuce. That can be good or bad depending on your weather. Given the small size of the bed you might want to do some reading over on the SQ. Foot Gardening forum here. It is a very different method than usual but lets you maximize your growing space when it is limited. And also keep in mind that lettuce has a limited season so it can easily be followed by planting another tomato plant in its space once the lettuce is finished. Dave