Can people ask their higher self to communicate useful information or help them solve a problem during sleep time, so they awaken with fresh inspirations and have a solution to a problem pop into their thoughts? If so, how is that accomplished?

This can be done quite readily. It is a normal part of learning, growth, and spiritual guidance in action. When you want something to come from divine realm, it is usually offered via way of the higher self. That is the normal mode of operating for each individual, that they have their onboard guidance, so to speak, the portion of the soul monitor assigned to them for their oversight and support. When you retire you can ask your higher self to assist you in working through a difficult issue or problem and the higher self will work with the deep subconscious mind to help reach an answer and to have it come into conscious awareness on awakening at some point—it might be immediately, it might be somewhat later in the day at an opportune moment, or when the thoughts return to having that particular issue, and then the answer comes. This is a common everyday occurrence people experience, not knowing the divine orchestration and the sequence of events involved. Having this resource available is wonderful to know about because it is often ignored and not implemented at all by people unaware that this is possible. So there are many lost opportunities for learning and growth simply for the asking.