As means "at the moment that something happened/happens," and it doesn't make sense here. It's not the he remembers only that one moment; he remembers the whole event, which covered more time than one moment.
While is normally used for an action in progress and is juxtaposed with another action of shorter duration, so it's not the appropriate choice for this sentence either.
2) Yes, you can use the present tense for remember. When used with the next verb in the -ing form, it means to remember something in the past.
Now, here's how your sentence needs to be corrected, my friend:
John remembers being more or less nine years old when he almost drowned underneath a raft in the middle of a pond.
drown is an intransitive verb, which is what we need to use here since we're talking only about what the subject did.
The preposition underneath is an option. It sounds better to use it here, but you can use just under if you'd like to.
The thing that swimmers/divers can stand on in the middle of a body of water like a lake or a pond is called a raft.
Since this is the first mention of the word pond, you need to use the indefinite article with it. If you mention pond again, you will change the article to the definite article, the.
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