If you can, think of a paragraph as like a hamburger.
This handout gives good information on paragraph development and unity.
Topic sentences are mini summaries of the paragraph to follow and, at the same time, relate to your thesis to help focus your paper.
Here are some examples of strong topic sentences: Topic Sentences (sjsu.edu)
Yes, it is true that writers must be careful not to introduce new points in the conclusion, but this does not mean the conclusion must just sum up points made previously in the body paragraphs. How boring! A good conclusion will explore the broader significance of your thesis. You’ll expand your thinking outward a bit. This is a handy page on conclusions that gives a good example: https://academicguides.waldenu.edu/writingcenter/writingprocess/conclusions
The overall structure of an essay with transitions may look something like this:
You can learn more about transitions HERE.