Hi,
It is said that the milky way, and the Andromeda galaxy are going to collide.
I have a few questions about this:
-How do you measure the distance to a deep sky object with an amateur telescope: we could use standard candles such as Cepheid s, but is it possible for us to make out individual stars with an 8" or 10"?

By anallising spectra and using the Doppler shift, we can know the acceleration of the andromeda galaxy towards us.
How can we measure it's mass?
Then how do we predict whether or not a collision is going to take place?
Also how do we know when the collision is going to take place?
According to newton's law of gravity the acceleration of Andromeda towards us will be increasing as the galaxy is getting near us.
But how do we know how the collision will work out?
For instance if both Andromeda and the milky way were orbiting a common center of mass, we could still see Andromeda "approaching us". How do we know that this is not the case?

(sorry for the bad english!!)

First things first. Your English is very good. Keep up the good work.

I don't think we could see individual Cepheids with a scope that size, let alone get good light curves. The work is done photographically with much larger telescopes.
We observe the Doppler shift on stars in different parts of the galaxy to estimate their orbital velocities around the center, and calculate the mass needed to account for that motion gravitationally.We can tell from the average Doppler shift that M31 already is approaching us, and once we estimate the masses of the two galaxies we can calculate the acceleration, and thus estimate the time needed to bring them together. Minimum separation, and possibly a collision, should be between 3 and 5 billion years from now.

The hard part is in estimating the transverse velocity, if any, because the motion is too slow to see with present technology. The experts are hoping to measure it within the next couple of decades. In the meantime they are doing computer simulations which predict an eventual merger even if they miss the first time around.

I don't understand your last question. Like any other pair of massive moving objects in close proximity, they are orbiting a common center of mass. The orbital dynamics experts have concluded that the minimum separation will be relatively small even if the transverse velocity is the most it likely can be considering the dynamics of the Local Group cluster. It is during the close approach that interactions become complex and a monster computer is needed to analyze the possibilities.

The October 2006 issue of Sky and Telescope has an extensive article which explains how the experts have estimated the situation. You may be able to find back issues in a large library somewhere.

You came to a good place to seek answers to questions such as yours. There are plenty of people who can do better than I can.