On Dragon Go Server I am finishing a game in the right corner white has a 2 eyes group but it seems to me that any move black makes to kill my intrusion will give me the chance to kill it anyways. Is the group white our are both parts alive?

http://www.dragongoserver.net/game.php?gid=909282

That position is called a Seki (See http://senseis.xmp.net/?Seki)

No Side can capture the other one so both sides are alive.

The score for that corner is 0 points for both sides.

So 'both are alive' is even wrong (although equivalent as that would give us both in this case 1 point?

No, it's considered both alive. In problem books for Go, seki is considered life, though it's of course better to have life without seki.

In Japanese scoring, neither player would have points, in Chinese scoring, both players would get one point in this situation.

IMO, a good (basically correct) answer is: Using Japanese rules, in your DGS game both players get one point of territory in the lower right corner due to the seki situation (both groups are alive).

If you had been playing with Chinese rules, in that corner the 10 white stones are alive so (including the one point in the eye) White has covered an area of 11 points; and I believe Black has covered an area of 3 points {two stones plus the one point (false-looking?) eye).

Seki is one of the Go / WeiQi situations in which the different rule sets can, and often do, give different results.  Take a look at:

http://www.math.unipd.it/~tullio/IS-1/Progetto/IGO/Go%20Rules%20Comparison.htm

To make it slightly less complicated, take a look at:

http://senseis.xmp.net/?Seki

and in particular:

Q.#7 looks like your DGS game seki:

http://senseis.xmp.net/?SekiWithEyesQuestion7

For a little more info, I suggest you also look here: Q.#4: http://senseis.xmp.net/?SekiWithEyesQuestion4

:)

In fact, AFAIK, under Japanese scoring seki eyes do not gain points. I recall that the stones are considered alive, but the area enclosed by stones in seki is not counted. Under Chinese rules the points are counted. Of course in your game position this does not make a difference, but there are many cases of seki where only one of the parties has an eye.