The -te form of taberu is tabete, not tabette.

If "kudasai" is omitted from a request, it is no longer a polite request, but rather a casual one. This is of course OK most times when you would say ganbatte (or ganbatte ne), but may be rude in some situations when you are asking someone to do something else.

To invite someone to do something politely, use the -masen form of the verb followed by "ka"; e.g. "tabemasen ka?"-- "Would you like to eat?"

Hajimemashite!
Thank you for the answers, I think I understand now and this is really interesting! But Tony-san, I didn't understand your 3rd example about [verb1] and [verb2] Are the words connected in a necessary way in this case?

And about -masen: There is this "Chotto tetsudatte itadakemasen ka"-flashcard I have and I really didn't understand why itadakemasu was negative (-masen) but know I see. But in this case, how do I know if it's negative or polite?? For example two people talking:
A: Tabemasen!
B: Tabemasen ka? Naze?
It's a verb so couldn't it mean NOT eat as well? Or can't you use it like this?

Keidawi-san, konban wa.

You can find more information on the -te form of a verb on the following page of the site:

http://www.studyjapanese.org/content/view/57/64/

This treatment is far from complete, however; you will probably have to consult a conversation or grammar text for a more complete answer.

There is often a causal connection between the verb in -te form, and a verb which follows it, but this is not necessary. It can describe simply an action preceding another action in time; but even this is not necessary.

In the example you gave of "tabemasen," it is clear from the context that the "tabemasen ka" really does mean "not eating." Context is everything. It is easy to construct examples in English as well where what a short phrase means can be completely changed by the context in which it is uttered. I think one should be wary of fixed translations-- especially translations of a single word by a single word-- and think instead in terms of usages. That is why I listed several ways the -te form could be used, rather than trying to say "what it really means." In many places, you will see the claim that the -te form of a Japanese verb corresponds to the -ing form of an English verb. This works for the use of -te to form progressive tenses, but it is clearly misleading for the other usages.

Some texts explain the invitation "Tabemasen ka?" by translating it as "Won't you (have something to) eat?", which is a possible invitation in English. But I feel that this begs the question, to some extent, as this way of making an invitation is apparently far more common in Japanese than this way of making an invitation in English.

Konban wa, Tony-san!
Allright, I see what you mean. Then it's exactly the same as in arabic in the "tabemasen"-case and I suspect in the -te-usage as well.

Thank you for the link!

Dou　itashimashite.

Please tell us about the ways of saying these things in Arabic. It would be interesting to see the comparison with another language, especially if there are similarities.

--Tony

Konban wa!
Oh, Dou itashimashite, does it mean "you welcome"?

And about the Arabic, I'll take the tabemasen-example again:

A: La aakill.
("La" roughly means "not"
B: La taakill? Limaathaa?
(here the "t" in "taakill" just indicates that it's about the person you're speaking to, so you don't have to add "you" in the beginning).

If you want to ask someone to eat you can also say "La taakill?". So it's like you said, Tony-san, it's all about context.
To make it even more funny (haha) you can say "La taakill." where you stress the "la". This means "Don't eat." X)

Thank you for your help!