So even if Bitcoin gets to a very skyhigh price, there will be no need to hold a whole Bitcoin to your self.
Settling aside the transactions. There is not enough Bitcoin for everybody and the scarcity that it has is one of the reason even if you don't hold a whole Bitcoin in the future, it will still get expensive due to halving, demand and its supply limit.
We can just make transactions and save in tiny fractions. so that's it, if Bitcoin had an unlimited supply like regular Money, it would lose purchasing power and value over time
Yes, it will only inflate if there's an unlimited supply. And this is the advantage that Bitcoin has, due to the limited supply that it has and also the limit will only be mined likely in 2140, it makes every satoshi that we own now very valuable if we hold it for a long time or until the next cycles.