Prevent and eliminate compaction, first of all. Step one!
Then, Organic Matter (AKA OM) is the magic solution to almost every soil texture problem. Too much sand? Add OM. Too much clay, add OM. DO NOT add sand to clay or clay to sand--you will more likely get concrete than usable soil, its expensive, a lot of labor and you'll never get it fully mixed, really. It mainly just makes a mess.
That said, OM isn't the be all and end all. LIVING OM is even better--a mix of plant roots of different kinds and diff kinds of leaf litter to help diversify the soil food web, these are very good. Fungi are also critical to soil health and maintaining soil porosity once it is established. The bacteria help make microaggregates of soil particles, the fungi make the mesoaggregates by binding the microagggregates together, and the soil arthropods and earthworms and folks like that make the mesoaggregates into macroaggregates that give the soil the crumbly texture we and our plants like. Gotta have that diverse soil food web. Diverse kinds of OM help diversify the soil food web (sounds like you are well on your way there). Diverse kinds of plants with diverse kinds of litter and diverse root structures also help a ton. I talk a lot about dealing with problem soils in EFG vol 2 chap 5.
Then there's biochar. Another huge topic. But this form of OM can remain stable in the soil for centuries, unlike other forms of OM which can decompose, along with the benefits of having it there. Biochar fosters all kinds of good things in the soil and will do so for a long time. MUST charge it with nutrients before adding it to the soil though, or it will suck nutrients out of the soil and away from your plants! Soak it in urine for a week or so, or use seaweed emulsion for that, or mix it with compost then apply that after a few days or weeks to let the char soak in the nutrients.
Getting this stuff into the ground: strategies will vary by intensity of use. Sheet mulching is good in close-in areas with intensive care and use, and forking or tilling in cover crops or manure/compost/biochar is not a bad thing in the early going to get soil texture issues and compaction resolved in such zones. Spot mulching further out, cover crops further away than that. Simple planting and leaving it to do its thing in even further away/less used zones. Get the picture? You seem to be on the right track. Just give it time and loving attention. It will improve.
Your second question has so many possible answers . . . You could pile junk cars there, for one thing!
Hazel hedges will easily withstand dog pee--they'll benefit from it, even. Or if you want something thornier, you could go with American plum (Prunus americana) or something similar. There are many many possible hedge plants to choose among. Or: need to put a shed somewhere? Trellis or arbor for shade? Really, the possibilities are almost endless. It comes down to what else you need to achieve and what elements or infrastructure do you also need on site that could serve a dual function? A water tank can offer privacy. A basketball hoop. A mound of earth. Do you want complete 100% view blockage or is filtered OK? Do you want air flow through or not? Is sound an issue too? Maybe you need a fountain or water tickle to confuse or lighten up the space while also blocking the view--maybe its more energetic than physical screening you need--a single tree trunk, rock, or post can define a space pretty dramatically if you place it well.
Take care and enjoy the spring, if you are in the N hemisphere, that is!