Do complete paragraphs start a new subject in the last sentence?

No. Change subject with a new paragraph.

No, each paragraph should be about the same subject. If you start a new subject, you need to start a new paragraph also.

Technically a new paragraph can be started whenever, but ideally a paragraph is about 7-9 sentences long. If the sentences are short or basic, then a few more sentences should be added to complete...

The last sentence of the entire essay, because you're concluding the entire thing. The first sentence of the last paragraph is called the introduction to the conclusion. (Complicated, right? :P)

When the topic sentence is last it is called a inverted triangle. The point being the topic, and the base being anything backing up the topic.