Is есть (eat/eating) a homonym to есть(meaning "is", also replacable by a -)
Yes. But the context will reveal the proper meaning. I don't think anyone would say "я хочу есть" and mean "I want to be." Rather, they are hungry!
Of course. And especially if we take into consideration that "I want to be" is "Я хочу быть" (not есть) in Russian.
By the way, do both expressions "I want to be" and "I want to live" mean the same in English?
Not really. "I want to live" means "я хочу жить",quite literally. "I want to be", on the other hand, is quite poetic and means something like "я хочу жить так, как мне хочется", i.e., do not interfere with my life choices. If someone points a gun at you, that would be a very poor choice of a sentence.
Есть means "to eat" AND happens to be used in the context of "у меня есть" as the third-person singular of "to be". I think of "у меня /есть/ что-нибудь" as "to me /there is/ something" or in better English, "I /have/ something."
But, you can tell by the context. The word есть in "Я хочу есть" and "Мама любит есть" is always going to mean "to eat." See Cute_Shark's comment above. And, "у меня есть ..." can always translate to "I have ..."
I would amend this by saying "у меня есть что-нибудь" is more like "at me/at my possession there is something."
It's not uncommon in other languages for possession to be treated as a virtual location at which objects can exist rather than a virtual container such as in English where things are in your possession rather than at it.
I still don't understand. I just wrote волк ест and it was correct, but Mama needs the soft sign for what reason?
The same reason as in English. "The wolf eats" and "mom likes to eat". "To eat" is an infinitive. The same is here. Есть is an infinitive while ест is 3rd person singular form.
I've noticed that Google Translator translates this sentence with Мама любит поесть i.e. it adds по in front of the infinitive. But for other verbs it doesn't do that, i.e. Мама любит пить
The question is: is Google Translator wrong or is there a meaning for this по?
There is a meaning, but I would really struggle to explain it. If I try to do it kind of short, then есть means consuming food or energy in a very broad sense, while поесть is more about the actual process, that you're sitting and eating, and plans of doing it.
For instance. Я хочу есть means I'm hungry. while Я хочу поесть, means that I'm hungry and I'm going to eat something. Then you can say Пойду поем. I'm on my way to eat something. But then, when you're actually eating you cannot use поем, instead you say Я ем.
So it's all vague already, but even worse is the fact that while
Я люблю есть is kind of the same as Я люблю поесть
Я люблю пить is not at all the same as Я люблю попить. The latter is not actually used. On the other hand, you can say Я люблю выпить, which means that you like to drink alcohol. o_0
I feel like I'm not being helpful here :)))) Maybe Shady_Arc will come and explain it one day.
But yes, if there is a difference between words, then it is there for some reason, there is almost always some difference in usage. Unfortunately such differences are not always easy to summarise in a clear set of rules.