There are just a few crater rims where this happens, not the full pole - but those do indeed get sunn almost all the time & border areas in perpetual darkness, which is also pretty useful (cryogenics, temperature gradient, etc.).
Sort of; there are some spots that get sunlight almost all the time. (The moon has quite a bit of wobble, so it's hard to get to 100%.) That greatly restricts your choice of base locations, though. There may be other resources or geological features you might want to be close to that aren't convenient (lava tubes, water deposits, flat places to land, minerals that can be used as building materials, etc...).
I suppose if our base is extensive enough, we could use those locations primarily for power generation and then transmit that power to more desirable locations for other tasks. Though I do realize that I'm talking about a lot of effort/time/money/resources.