How closely related will your descendants be to you?
For how genetically related to you your  my grand-grand-children will be....

Well on the surface the answer is simple. Your grand grand children will 12.5% of your DNA. 

Dig a little deeper... the question becomes a bit more difficult to answer.

(1) Humans do cheat a small but significantly amount of time. On average about 0.7-3% of all children are unknowingly raised by men who are not their biological father http://theconversation.com/what-are-the-chances-that-your-dad-isnt-your-father-24802. This is less than the 9-30% which has been reported. The reason appears to be that the data was derived from paternity clinics where  there was already suspicion on paternity of the child. Not the best data set to represent the population, even if the data set was large and mostly free to researchers.

So which that factored in... it depend on what gender you are, and how said grand grand child is related to you. Are you a woman? Is that grand grand child, the child of your daughter's daughter. A pure maternal descended would guarantee a 12.5% genetic relatedness. 

But if you are a man, and the grand grand child, is the child of your son's, son... on average genetic relatedness falls to 11-12% (on average). But since a person is related to your or not, there is a 3%-10% that your grand grand child is not related to you if that child is your son's son's child. 

(2)Rural (old world) populations tend to share more genetic material since they have had less outside influence into the genepool. This is a reflection of history, where mobility was limited and families tend to stay for generations. In these places, a random stranger isn't that random after all. In which case genetic relatedness calculations become more complicated. Terms to look up are founder effect, population structure. Large cities, with massive influx of people moving in and out tend to be more mixed. Also note isolation, can also because by social stratification. The nobility is a great example where two random nobles are not as random as you think.

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1685612/pdf/ajhg00202-0030.pdf
http://link.springer.com/article/10.1007/BF02442864
http://www.nytimes.com/2004/07/31/us/by-accident-utah-is-proving-an-ideal-genetic-laboratory.html rare american example.
https://en.wikipedia.org/wiki/Stoccareddo
http://gizmodo.com/5882644/iceland-is-so-inbred-it-needs-a-website-to-avoid-incest


  And I also once heard that even though the share of my genes will be
  descreasing, the mutations unique to me will stay. Is that so and how
  is that possible?


Not quite. A mutation unique to you has only 50% chance of passing on to a child. (Or a 50% chance of not passing to a child.) So if you have 2 children, that mutation will have a (0.5*0.5=0.25) 25% chance of failing to pass to the next generation. In fact unless that mutation has some sort of selective advantage (awesome X-men powers), or your family has really big families for several generation or you and your families becomes a founder of a new colony/town (founder effect), your unique mutation will likely fallout after a few generations. 


  And what about all-males descendants? Like, if I have a son and he has
  XY, then if there always will be a son down the line then Y chromosome
  is going to stay the same, being the one from me?


yeah they will inherit your Y chromosome.. which will change very little over the generations. It will accumulate a few mutations but that is over thousands of years.