Please clarify - you only received one K-1, correct?
For "Part 1" of your question - If the "master K-1" reported income in more than one line, then you have to complete a separate K-1 interview for each line - just as you described above.
For "Part 2" of your question - You do not need to make separate K-1 entries for lower-tier partnerships reported in the supplemental information; that information is already in the "master K-1".
If selling a partial interest, you can report that sale in any one of the K-1 interviews you had to do because of multiple types of income.
Reporting the sale of a PTP is complicated. The following post provides detailed instructions on how to accomplish this. Look at the first answer for instructions, and then look at the follow-on replies for additional information.
Reporting Sale of publicly-traded limited partnerships
