Hi!

Could anybody please tell me what it is the form: ver misin. The tea lady in our company is always told, "çay ver misin?" I don't know the exact translation but of course it means "will you bring tea".

I have checked my tr language book but still not sure, maybe it is istek kipi (optative mood)?

Also is it polite enough to ask for sth like this?

Hi,

"çay ver misin?" doesn't exist.

It can be one of those:

"Çay içer misin?" Would you like to drink a tea?
"Çay ister misin?" Would you like to have a tea?

'içer' is the simple present conjugation of içmek.
'ister' is the simple present conjugation of iistemek.

It is more polite to speak in plurals. These are preferable:

"Çay içer misiniz?"
"Çay ister misiniz?"

These are common answers in this case:

"Evet, lütfen."
"Yes, please."

"Hayır, teşekkür ederim."
"No, thank you."

maybe i just misheard, but seems everybody here who wants tea asks for it like that...

how could they ask then, if my version is wrong?

Oh, I see. I thought the the lady asks people whether or not they want tea. If people ask the tea lady than this is what they say:

"Çay verir misin?"
"Can you give me a tea."

'Verir' is a conjugation or 'vermek' (to give).

This is not actually a very polite way of asking for something. It sounds a little patronising to me.
A more polite version would be :

"Bir çay alabilir miyim lütfen?"
"Can I have a tea please."

as far as i can understand, the structure is like this:

ala > almak (to get)
bilir > can
miyim > indicates the question and refers to the person asking

doğru mu?

Well, your approach was very logical. You almost got it right. It is like this:

"alabilir miyim"
al / abil / ir / mi / y / im

1. 'al' is the verb stem of 'almak'.
2. 'abil' (or 'ebil') is the abilitative suffix. It has an etymological connection with bilmek as you guessed.
3. 'ir' is simple present tense. Instead simple present (which is the most common with ebil) you could use another tense: "gelebildi mi?", "gelebiliyor mu?", "gelebilmiş mi?"
4. mi is the question suffix.
5. -y is buffer letter that comes inbetween two vowels.
6. -im is personal suffix taken from this list:

Singular
1. : -ım, -im, -um, -üm
2. : -sın, -sin, -sun, -sün
3. : --
Plural
1. : -ız, -iz, -uz, -üz
2. : -sınız, -siniz, -sunuz, -sünüz
3. : -lar, -ler

teşekkür ederim erdinç