Learn English – suggests that she sit /sits/sat

He said with didn't you don't use another past verb form.

This is a good heuristic, though I don't recall anything about "double past" in school myself. But it still works.

The technical way to say it is "do can take an auxillary/helping verb, but the only valid auxillary/helping verb for do is the plain or infinitive form (same as present tense)."

She would hold my bicycle from the back to ensure that I don't fell down.

The one you say is correct -

She would hold my bicycle from the back to ensure that I didn't fell down.

is still not correct (if someone told you it was, they are wrong).

Following your heuristic, the right answer is:

She would hold my bicycle fro mthe back to ensure that I didn't fall down.

To start

To review by region

These are phrases not clauses. They are infinitive phrases with "to" as the marker and the infinitive form of the verb (the first entry in the dictionary) start, review. Infinitive phrases can act as either a noun or an adjective or an adverb, depending on how they are used in the sentence.

You can start a sentence several different ways, and two of them are with either an adjective or an adverb:

Angry, he threw the glass down on the floor.

Unfortunately, that is not true.

And the same goes for infinitive phrases. Keep in mind an infinitive phrase can be more than "to find" or "to ask" etc. It can have complements and modifiers too: To review by region [by region is a prepositional phrase modifying "review"]. Sometimes the marker "to" is omitted and understood: I'll help you wash the dishes. = I'll help you (to) wash the dishes.

See page 78.

http://images.pcmac.org/SiSFiles/Schools/AL/HooverCity/SpainParkHigh/Uploads/Forms/Start%20Holt%20Handbook%2010.pdf

http://www.grammar-monster.com/glossary/infinitive_form.htm

http://www.grammar-monster.com/glossary/infinitive_phrase.htm