Seat aisles blocked by baggage

You are right to ask about safety-related issues, and of course a passenger has every right to inquire about or report such things, though I would first seek clarification from the cabin crew or airline.

That said, most of the "outrageous" things you'll see (wether live or on the internet), are actually perfectly safe, as for example fixing minor problems with speed tape

Regulations

As for your question, it is impossible to answer what the regulations are on your flight without knowing the exact procedures of that particular airline for that particular type of aircraft. So unless some A320-Lufthansa cabin crew pitches in, we'll probably not get a definitive answer.

In their passenger-facing documentation Lufthansa suggest to put laptop bags and such under the seat, and trolley luggage into the bins. But that doesn't mean their internal rules don't allow larger items.

The FAA has some information on cabin safety, which gives some insights into the general guidelines. These will probably be the same, or very similar, in Europe. Note that they refer several times to the "airlines carry-on baggage program", indicating that the airline will have to provide the specifics.

It is a bit moot to discuss the safety card: They are not meant to be a exact diagram on the maximum dimensions of items under the seat.

A note on terminology: The "aisle" is the walkway in the middle of the plane. It does not refer to rows of seats or the space between them - this was confusing in the initial question and needs to be understood when reading the safety regulations.

Even according to your explanation, the aisle of the aircraft was never blocked.

Is it safe?

The FAA guide gives some insight in what safe: The baggage must be stowed in designated places, not obstruct emergency equipment and not obstruct movement through, or to and from, the aisle, and the luggage must not move around.

• The picture of the roll-on luggage seems to indicate that is safe. It fits under the seat, and does not potrude behind the "feet" of the seat, which are usually about as far back as the backrest of the seat. The luggage is secured on all sides and won't impede your exit from the seat much more than the "feet" do. I realise that this configuration leaves you with no legroom and is crazy uncomfortable, but that, in itself, doesn't make it unsafe.
• The picture of the handbag does seem to show it isn't stowed completely properly and may come lose or impede movement. It looks like it could fit, though. We do not know when this picture was taken and if they were told to stow it correctly later on.
• The "business class" announcement sounds like a misunderstanding to me - it is pretty normal to ask them to stow thing "in the space under the free seat", and that is most likely what they meant. Of course bags must never be stowed on seats, and it seems very unlikely that the crew would ever allow this to happen. According to your original question, we have no indication that it did.

Can they do that?

Part of your question seems to be wether it is likely that the cabin crew of a major European airline would regularly flaunt safety regulations. The answer is, most likely, no.

The airline industry is highly regulated, and crews are regularly and specifically trained on this. While some may be more relaxed about things, any flight attendant who intentionally goes against safety regulations risks to be fired, or worse, especially when doing so in a public, obvious way. And no airline would ever officially permit such conduct.

So in your situation it seems they had much to lose, but apparently nothing to gain, by going against regulations.

To me it seems more that the crew prioritised an on-time departure over the comfort of (some) passengers.