"Hello! My last name is Li."
For this sentence there was only one option for Li, but it had another word before it and then marked it wrong.
[你好] [我] [姓李] was marked correct for me, but 姓李 shouldn't be one word. Reported (but as "dictionary hints are missing", because there's no option to report segmentation errors)
的 (de) is used to indicate possession, but it's normally omitted when talking about family, such as your relative or family name
The word '李' was not under the option available, so I chose '姓李' which was not correct. This should be changed to be correct at the very least, or 李 should be added as a possible word.
It is common, yes. If you introduce yourself and tell someone your whole name, you tend to say your last name first (this isn't just in Chinese, either).