Correct English can have the adverb before or after the verb. So, you have to look at the sentence and ask questions about sense, ease and ambiguity. For example, if one were to say:
He ran quickly.
This implies he ran quickly as opposed to slowly. However, when one says:
He quickly ran.
This implies that he ran instead of walking, or it could mean that he was doing something else and then suddenly, very quickly, he began running.
You just have to look at the situation and ask yourself which sounds better, which makes the most sense in the manner you intend, or what flows with the greatest ease..
If it is preceded by the word "to", this is a different story. If you had a sentence that was:
He started to quickly run.
This is actually what is called a "split infinitive". An infinitive is simply a verb with the word "to" preceding it: to walk, to see, to hear. You want to keep the "to" and the verb together and not split them apart, hence the term "split infinite".
Just remember that any time you have the word "to" and a verb following, don't put anything between them. That is a good rule of thumb and easier than remembering the definition of a split infinitive.
The correct verses will be: (1) he ran quickly and/or (2) he runs quickly.
"Is run" is correct. "Is ran" is not grammatically correct.
'To run as quickly as possible' is 'to sprint' or 'to dash'.
Run away. Quickly.
Sam will run, and run, and run.
Had run is correct.
Have run is the correct present perfect tense. Perfect tenses are created with past participles, and the past participle of run is run.
"Would have run" is correct grammar. "Would of run" is a common error known as a homophonic mistake, where "of" is mistakenly used instead of "have."
The first one: "He kept wanting to run" is correct.
The correct phrase is "you have run." "Run" is the past participle form of the verb "to run" when used in perfect tenses with the auxiliary verb "have."
I will run you over.
The likely word is gallop (a fast speed on horseback, to run quickly).