How are cryptocurrencies even worthy when I can’t feel them like a $100 bill?

This is the most common argument when talking to people about cryptocurrency, mostly because it is not easy to understand the evaluation of this asset.
My first response: Why is money worth anything? It is just paper or digits in your bank account. It has no utilities; you cannot eat it, drive it or sleep beneath it.
Money is worth something simply because we acknowledge its value as a means of trade, with which we can exchange goods or services.
Similarly, cryptocurrencies are worth something because we agree that they are. In many ways, they’re much more practical than traditional storage of value, such as gold. Bitcoin has a fixed volume, at one point no more will ever be made, so it will not be subject to inflation and risk of devaluation. Bitcoin and Ethereum are anti-fragile, impossible to destroy. Every single Bitcoin created since 2009 still exists.

Where is the Federal Reserve Bank for cryptocurrencies?

Decentralization is crucial for cryptocurrencies. Decentralized means that every user on the network has a vote in what direction the currency will develop. It means that the more computing power you provide to the network, the more votes you will have. No single entity can control more than 50% of the computing power in a developed cryptocurrency because of this, the users of currency are in power of the currency. Which makes controlling them, truly democratic.
Another fundamental cornerstone of good cryptocurrency is an open source code, giving users the ability to review the code to make sure the developers haven’t created one that allows them to violate the terms of initial agreements.

If it’s online and virtual, doesn’t that make it hackable?

There are multiple ways to store your cryptocurrency, some safer than others. The simplest way is to use an online wallet. Here, you trust a third party to store your currency for you. To access your money, you can simply login over a web browser. Using the 2-factor authentication which every good online wallet offers, is an easy way to keep off hacking via keyloggers or trojan horses. Hackers are thus unable to access your account without your secondary device (usually a smart-phone) on which you receive a temporary code you can use to log in.

Websites being attacked is very rare now due to better encryption and most sites store majority of their currencies offline.
A more secure way to store your cryptocurrencies is in a paper or, my personal preference, a hardware-wallet which allows you to store your Bitcoin or Ethereum offline and out of reach for hackers. They can be reached through a hardware device which you can carry on yourself and can only be accessed through an 8-digit pin-code.