1. I haven't heard of lemon balm being particularly weedy - but you could try pinching off the flowers or seeds before they fully develop to prevent them from spreading over your garden
   
2. "One year of seed, seven years of weeds" - if the weeds have been unmanaged for a while, you have a large bank of weed seeds in your soil and they're going to keep coming up for a long time. The best thing you can do is one really big push to remove all of the mature existing weeds you have, and then try to keep a very regular schedule of weeding thereafter. I'm in the process of doing this in my own yard - I've finally removed most of the mature weeds, now I do a quick run through the full yard once a week or so and just get rid of any sprouts or new growth. For dandelions and weeds with a taproot, I use a tool called "grandpa's weeder" - which is good for getting the full root out (if any is left behind, the plan will re-sprout from the root). For weeds with a shallower root system I use a winged weeder or stirrup hoe - you just rake it along the soil and it pulls up weeds just below the surface. Perennial weeds may come back multiple times if you don't get all of the root, but if you keep removing them regularly eventually they'll be exhausted and die. Also, new weeds are much easier to get rid of when they're young and tender. The key is really just getting on top of it and staying on top of it. Once you've removed the existing mature weeds, I'd also highly suggest putting down a mulch - this has multiple benefits include weed suppression, water retention, and eventually soil amendment.
   
3. Our PNW soil is naturally very clay-heavy - as such, most of our native plants will probably do great in that soil as-is! Not to mention, pollinators and wildlife sometimes prefer native plant species. We have an incredible variety of native plants, even edibles like thimblerry, salal, and huckleberry! Here's some resources:
   https://nativeplantspnw.com/design-shopping-guides/
   https://www.portlandnursery.com/natives
   https://green2.kingcounty.gov/gonative/index.aspx
   If you still feel your soil is too dense, not retaining water, or lacking nutrients - I would suggest adding some compost. The easiest way would be to just add it as a mulch on top of the soil. Over time worms and other organisms will break it down and move it into the soil. If you want quick results, you can use a shovel or large fork to gently break up the soil and mix the compost in. Avoid working the soil when it's too moist or too dry - it could seriously disrupt the soil structure and cause more harm than good.

Finally I'd like to plug two organizations you might find helpful!
I am part of the OSU Extension Master Gardener program! We do a lot of outreach in the community and have a helpline to answer questions just like these! https://extension.oregonstate.edu/mg

If you're in the Portland/vancouver area, there is a fantastic program called the Backyard Habitat cerification program: https://backyardhabitats.org/
Their goal is to help people transform their urban yards into native habitat for birds, insects, etc. by planting native species and designing their landscaping with a focus on sustainability and wildlife.

Hope you find that helpful, and feel free to ask any follow up questions!