Is it considered cheating for a student to copy solutions to homework assignments available from resources or the internet and submit them to the teacher, knowing that it is not an exam? And is evaluating the teacher's explanation level as bad or deficient considered backbiting?

Cheating depends on what the university administration or the professor permits. If they allow the use of books or the internet, then there is no harm in it. However, if they do not permit it, then doing so is forbidden cheating, based on the Prophet's (peace be upon him) saying: "Whoever cheats us is not of us." As for describing the teacher as negligent or having poor شرح (explanation), it is forbidden backbiting unless it is for a legitimate Sharia purpose, such as filing a complaint.