Those are legitimate questions. I'm not a cryptography expert but I think I can partly answer.
First of all, this looks like a communication coup more than anything else. Now and then people who try to develop quantum computers do such an operation to raise funds. It's been so since dozens of years.
Here, the paper has been conveniently "released" in a way that bypasses peer review. You can bet that serious review will seriously tune down the expectations.
The information from the articles doesn't match together, and they are written in a way that is meant to excite the imagination and induce the reader to misinterpret the situation. The third article, in particular, is full of inaccuracy, misunderstandings and goes totally off track with the GOD-is-an-IA thing.
The conclusion that "2048-bit code-breaking could be achieved in mere seconds within two years." is erroneous. NASA said that at that point, they could only link qubits by groups of 7. They would need to link them all to achieve a real quantum processor. So they are stuck on a serious technical problem here.
Now, you're right in stating that quantum computing is a threat for asymmetric cryptography, and this is why solutions are being worked out since years. But not all cryptographic functions are weak to quantum computing: for example, hashes are not.
This is why, in the early days of Bitcoin, Satoshi Nakamoto introduced a change to hide public keys stored in UTXO behind two cryptographic hash functions. This way, accounts are safe against quantum computing until the first time funds are moved.
So to summarize: we still have plenty of time and it's not going to be as dramatic as it seems. But yes, this needs to be addressed seriously.
Are we to be concerned about our privacy?
Yes, as most encrypted peer-to-peer communications rely on asymmetric cryptography. We already know that agencies such as the NSA are storing those in big data centers, waiting for the day they can break the encryption.
Even excluding quantum computing, asymmetric cryptography never was about hiding a secret forever - but only for a long period (20+ years). Unfortunately, the marketing around secure communications often forgets to state that fact.
Will Google be able to steal our Cryptos?
Only from incompetent projects, as a legitimate project will likely implement protections in time. It will be a mess, but we'll go through. What will happen on the user side is that we will all have to either update our signing keys or move our funds to quantum-safe accounts.
When it comes to big players stealing crypto, remember that many so-called "secure" wallets store private keys right on Google/Amazon/Microsoft/... servers without encrypting them before sending (they let the cloud service deal with encryption). This means that Google & such already have a lot of keys at their disposal.
Can we keep anything safe and secret from the (ideological/military) enemies?
There are still challenges to be solved before we have a fully functional quantum-resistant cryptography. But most likely we'll get there before them. Even the military needs reliable encryption.