Absolutely, cryptocurrencies posses all the attributes of money. Money is anything that is universally accepted to be representative of value and trust. Bitcoin has attained the universal acceptance as a representation of value and there are several use cases of Bitcoin as a medium of exchange across the global. Bitcoin represents a better and valuable monetary system than the current fiat system that is not backed by anything of value. Since the depegging of fiat off the gold standard, paper money is only backed by central govt authority and thus subject to manipulation by the same authorities.
Asking about whether crypto assets have normal asset attributes is equivalent to asking about the value proposition of crypto i.e Bitcoin. Bitcoin has very unique utility fundamentals and value cores established by the process of its creation (mining), it has a definite supply and cannot be duplicated just like any other valuable asset. All assets experience up and down turns owing to the investor confidence in the particular asset and the same metrics determine the price of crypto assets.