Thank you for your inquiry.
Yes these boots are fully waterproof, they use a waterproof Gore-Tex membrane which will keep your feet dry until you step into water deeper than the height of the boot. You can find the weight by clicking on the "Specs" section. They weigh 18.6 oz which is just over 1 lb per boot. This weight is for the sample size, which is 9 US, so it will vary slightly with different sizes but it is enough to give you an idea of how heavy they are.
It is difficult to recommend a size since I don't know how much room you typically have in your running shoes or how thick or type of sock you plan on using in your boots. Modern wool socks generally come in 3 different thicknesses and are very different from older thicker traditional wool socks. With all that being said, most of the time your typical shoe size fits well. If you are going to use heavy, really thick socks then maybe go up half a size. One risk of increasing size just because of sock thickness is that once your socks compress your fit can become sloppy, causing blisters and sacrificing stability. Since you wear a US 10 the La Sportiva 43 converts to a US 10 and also the 43.5 converts to a US10.5.
I hope this has been helpful for you, please don't hesitate to contact us with any further questions. Have a great day!