1. How can we trust the genuity that bitcoing will attain the height proposed for it?
What proposed price? Not even Satoshi gave an anticipated price. Any proposed price is based on individuals and their speculations. Some hope for 50k, some 100k, etc,
2. This fluctuations observed in bitcoin, can it make it stand the test of other currency?
I'm not sure that Bitcoin is doing a competition with any other currency. The fluctuations is normal, it is not a new thing. In fact, it is the nature of Bitcoin to fluctuate. People even make good money buying Bitcoin because of the fluctuations.
3. The irregularity and unstable price of it observed, can it still make it the world's best currency which will be widely accepted?
Bitcoin is not striving to be the world's best currency. Bitcoin is rather a digital currency that gives people the chance to rule over their money, and not falling under the canopy of the corrupt centralized system. As it stands now, Bitcoin is already serving that purpose, and have even lead to the creation of over 10k altcoins/tokens. Unstable price can affect it functioning as a payment option but, we can't remould it but use it the way it has been given to us.
Oh yes, with all this questions running in the mind of investors, there is still an assurance that the bitcoin we know and are trading will still retain it's place and make more wave than the previous trend which has been.
I believe that no one has money to waste. Investors must have done their research before investing. Eventually, patience pays a lot in crypto.