Can additional sugar help yeast consume the Oxygen present in the bottle? What about isobar systems with counter-pressure? What happens to the oxygen in the bottles? Does it have an impact on beer conservation (stability)?
"Can additional sugar help yeast consume the Oxygen present in the bottle?"
Yes, although in actuality yeast needs oxygen to grow/divide. So the standard aerobic action of yeast is to use oxygen and other nutrients to grow. When the oxygen is used up the growth phase is minimised.
What about isobar systems with counter-pressure?
yes, what about them? If used correctly they can be used to fill containers under a suitably inert atmosphere like nitrogen or carbon dioxide. They prevent the beverage coming into excessive contact with oxygen (or whatever...)
What happen to the oxygen in the bottles? Does it have an impact on beer conservation?
It would seem to depend on the nature of the beer. I have had no problem home bottling thousands of bottles of beer over the last decade using a siphon tube in air after pouring the beer onto the priming solution in a 50L bucket (with all the aeration that entails). It seems the yeast still in solution uses the oxygen to multiply and produce an anaerobic environment in the bottle. Once that is achieved, the carbonation proceeds to completion and the (unopened) bottle can safely stand for some years. On the other hand, "commercial brewers" seem to have a real phobia about oxygen in the brew, post fermentation. I am not sure why that is but it may be down to filtration or pasteurisation that can remove the yeast or render the yeast inactive. Whatever, commercial breweries seem to taker great pains over excluding oxygen. Perhaps it is down to the fact that Oxygen reacts differently with live things and dead things. Perhaps live beer is more stable and conditions in bottles/barrels more predictably. Perhaps filtered or pasteurised beer is more susceptible to other factors because it has no stable biome to hold the equilibrium. In such a situation the oxygen might react in ways that are less useful and completely different to the way it might react in an active yeast solution. All I can say is that oxygen in bottles is not instant death for the beer contained within. I have many bottles of beer made and bottled in "less than oxygen free conditions" which are over a year old and still taste great.
I know I will attract some "adverse comments" for espousing this view. Of course there is much literature that seems to imply that oxygen (or any similar oxidising agent) is so bad for beer that one wonders how they ever made it back in those slightly less than totally aseptic Saxon Ale houses. Was beer only drinkable after bottles of CO2 went on sale? Well that is something for the reader to consider but I also add this point. If oxygen was so bad for beer why do some breweries recommend using N2O as a gassing agent for their beer (eg some Irish Cream ales, etc). N2O is a known oxygenating agent and presumably (if all the phobias were well founded) would kill the beer dead from 20 yards. But no - the flavour (apparently) improves and makes the brew taste sweeter.