Not able to Replenish Water Supplies

To get unlimited, clean water in your city - build your sewage plant next to your water filtration plant. This is how they do it in real life, too. The sewage pumps filter the water and dump it directly in the ground. Your water plant doesn't need the fancy filtration pumps, only need the basic water pumps because the sewage treatment plant will have already filtered the water. I do this with every city and it works every time. An alternative is the Cities of Tomorrow expansion, which gives you the opportunity to research a sewage filtration plant that will turn the sewage into potable water.

Reclaim radioactive ground - The base game was designed to mimic real life situations; to get rid of it takes decades of Sim-years of planting trees over and over in the area. It's the only thing that will clear it up, and it takes something like 34 Sim-years per level of radiation. (Think of Chernobyl irl; still not "cleaned"). It's a real hassle, and takes a lot of dedication to get it done. Just a note - for a long time I didn't know where to find the "plant trees" thing, so in case you didn't know - go to the Parks menu, Nature ($$) tab and scroll all the way to the end to find the Plant Forest option. If you go this route, de-zone the area so you're not constantly bulldozing. Weirdly, I've heard that you can plop buildings such as schools on the radiated spot without a problem. If I were you, I would probably try plopping the garbage dump there. You can plant trees all over the dump zones, which is the way to clear up ground pollution as well. A faster solution is the CoT expansion again, which has an Academy research option to unlock ground scrubbers. These work really well and will clean it all up in a matter of Sim-months.

Neither of these problems are bugs; they are working as designed and just take some creativity or due diligence to work through. And of course, the expansion pack makes it faster and easier but it's not required. I personally prefer the sewage-water plant technique rather than the expansion pack upgrade because it's cheaper and I can start the city with them working together, rather than waiting on the Academy research. Otoh, I believe the ground scrubbers are worth the cost of the entire CoT expansion pack.

Hope this helps!