As they say, everything counts in large amounts
But before I proceed, I want to make it clear from the beginning that I fully embrace and endorse the tenets and notions of the subjective theory of value which basically claims that there is no intrinsic or inherent value in anything as all value comes from utility, i.e. a capacity of being useful for satisfying certain needs or attaining certain ends. The amount of this capacity obviously depends on how we use or think we can use something to our advantage. In simple terms, all value exists purely subjectively in our heads and comes about through our assessment of something and its usefulness to us (so-called marginal utility)
With that said, this notion of all value being entirely subjective is often sort of overkill for most practical intents and purposes, and we can safely go along with an assumption that there is a certain intrinsic value in things. In case of money, conceptually, it is transactional utility which can be defined as a capacity for transferring value, conveniently and reliably. In essence, this is what makes money into money. From this point of view, Bitcoin can do the job pretty damn well as it is state-agnostic and trustless. Given the nascent technologies like Lightning Network, Bitcoin has a lot of potential and plenty of space for gaining more transactional utility just around the corner
They also say that Bitcoin is a survivor and this post explains why exactly. No matter how low the price can go and for how long, it won't lose its capacity for transferring value, i.e. its transactional utility, as it is built in and will remain there unless Bitcoin is destroyed completely or its network compromised beyond repair. Ultimately, it doesn't depend on market price and speculation as it is rather a matter of how fast, cheap and reliable you can transact with Bitcoin. All in all, its price has little to do or interfere with this capacity. That's the reason why Bitcoin is here to stay and why it may in fact be a good day to buy hard these days
Feel free to share your opinion below if you have any comments, ideas, maybe even a few satoshis of criticism (in a constructive and helpful way)
So what exactly are you trying to say here
Maybe, that Bitcoin is here to stay (thanks to its transactional utility)?
Regarding your other questions, you may want to read my previous posts on this matter. As I always say in such cases, money is what money does. So if something is used for trasferring value on a wide enough scale, it is money, as simple as it gets. If you feel lost or have doubts as to whether something can be called money, use this simple, rule of thumb definition. If we define transactional utility as a specific quality attributable to money (something intrinsic to money), we can as easily use this definition in reverse, i.e. if something has enough transactional utility (e.g. in the exchange of goods), we have all reasons to consider it money
Oh, and yes, Bitcoin can in fact be used both offline and offchain, with Lightning Network, for example. Once fully activated, it will add dramatically to Bitcoin's transactional utility. It looks like we are on the verge of revolutionary changes in global finances, and that explains why Bitcoin is changing pants (corrected) hands right now