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"Amar é passar a vida inteira dedicando-se à pessoa amada."

"Amar" because they're trying to define a word, so they use the dicionary form
"é" because of the same thing above xD
the third I didn't understand '-'

Hi 小聪聪-Francisco,
1) In this case I think you can use Amor too, but the autor seems try define the verb "Amar"
2)
First question: The same above
Second question:
You have to analise the context.
"Ser+Fazer" the verb "Ser" is used to define characteristics of something. Examples: I'm tall, I'm smart.
The verb "Fazer" is used to define what are you doing/making. Examples: I'm doing my homework, I make a joke.
The verb "Estar" is used when you trying to define the situation of something. Examples: I'm Hungry, My pc is broken
3) I didn't understand what you mean.

I hope you understand, I'm learning English.
Enjoy your studies.

First, I will do a rough translation for you;

“To love is to spend your whole life dedicating yourself to the loved one.”

Amor is a noun, it's the feeling of affection for someone/something; while amar means “to love”, it's a verb, the act of loving someone/something.

Yes, ser + fazer is a common occurrence, you might want to take a look at Portuguese non-finite verbs, in this case impersonal non-finite (Infinitivo Impessoal). Yes, it is a difficult topic to get a good grasp of, even linguists have a hard time with them. That's not a reason to give up, of course. :)

Estar fazendo is the same thing, it's a non-finite verb called gerundive.