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Everything is correct in your source.

Подать is perfective.
Past Tense: подал;
Present Tense does not exist (since it is perfective);
Future Tense: подаст.

Подавать is its imperfective pair....

I'd say everything's correct except a slight nuance with "не надо" phrase.

I think "не надо" can have two shades of meaning, so it can be a bit ambiguous sometimes.

1. "не надо" can express...

A great link, thanks!

A verb has conjugation (спряжение), a noun has declension (склонение). We conjugate verbs, and we decline nouns.
So, it should read "a verb with incomplete conjugation".

Yes, it is incomplete:
...

I don't think it sounds good.

1. "чтобы" adds the meaning of "in order to", it indicates a purpose. It's useful when you do Action 1 in order to perform Action 2.
As in the example above, I was...

My try:

1. Не строй из себя дурака. (Literally: do not build a fool of yourself).
2. Старайся выглядеть умнее. (Literally: try to look smarter).

That's the other way around:

подходить (imperfective) is more like "to be approaching"
подойти (perfective) is more like "to have approached"

But they are not exact definitions, just...

No, it is not. It is the infinitive form, and the infinitive form does not have any grammar tense.
But it has the aspect: "подойти" is a perfective verb (as bitpicker noticed).

Perfective verbs...

Living

Yes, we have some strange rules for the grammatical animacy.
"Покойник" (the deceased) and "мертвец" (dead man) are animate: Он увидел покойника. Он увидел мертвеца. But "труп" (corpse) is...