The concepts are quite simple. Spend less than you earn and save the difference. To help keep expenses low pay attention to the big things: live close to work, or work close to home to keep communing expenses low. Use the money to buy productive things: rental properties, or stocks. That gets you more than 90% of the way, the rest is where best to put your money considering tax advantages, and drawbacks of different accounts.
I think your time is better spent figuring out what savings and retirement vehicles are available in your own country than trying to equate them to options available to a person living in USA. You might find someone from your mysterious European country here who could help with that, if you tell us where it is.
A 401K account provides a way to save on income taxes while you work, and allows investments to grow without capital gains taxes. It's an optional account, and the money in it is yours to keep. It's subject to extra taxes if not withdrawn according to some rules. What you're comparing it to sounds very different, so the benefits and drawbacks would be different.
Also, from what I can see, no European country has a retirement age of 70:
https://en.wikipedia.org/wiki/Retirement_in_Europe , so I'm not sure if you're being pessimistic about the pension being there when you need it, or what.
I would not factor your parent's house into any FIRE calculation because:
1) By the time you inherit the house, it may need lots of work
2) They may need to sell the house and move in with you if their finances don't work out
3) If you're really looking to FIRE, you'll want to be job-independent before your parents pass away