Pension in the EU when having worked in multiple European countries

I have a few questions about (state) pension plans when having worked in multiple EU countries in your lifetime. First off, EU countries have different requirements in terms of minimum years worked/payed to be eligible for a pension, age of retirement, and how one’s pension is calculated. Two examples:

The German pension system is working based on points, where earning an average German salary in a year will award you with one "point". Each point is "worth" a certain amount of money in the end, where this amount is adjusted every year (to compensate for the increase of the average salary/inflation). You retire at the age of 67.

1. 5 years minimum
2. Retirement age 67
3. You collect points

The Portuguese system requires one to pay into the system for 15 years to be eligible for a pension, which you collect at the age of 66. The system is working based on years and average salaries you earned (if I understood correctly). When retiring, you will receive 2% of your average salary times the number of years you payed into the system.

1. 15 years minimum
2. Retirement age 66
3. You collect average salaries and total years worked

Now how are these systems working "together" if one would "jump" between countries in the middle of one’s working life?

1. Assuming having worked the minimum number of years worked in ONE country, but not in others – how is this exactly calculated and handled? As fas as I understood, you have to apply for my pension in the country you are living in, which will then automatically (?) calculate your pension from ALL EU member states.

2. Am I correct in the assumption that having worked in a EU member state for less than the minimum amount of years required for the local pension still allows you to collect the pension from that state if you have worked the minimum amount of years in another state?

"The possibility of including contribution periods recorded in another
EU country or in another country where European regulations apply is
relevant to payment […]" (https://ec.europa.eu/social/main.jsp?catId=1125&langId=en&intPageId=4744)

3. The statement above is from the EU. Am I interpreting this correctly when assuming that if I apply for my pension in a EU member state A in which I have worked in, but HAVE NOT the minimum amount of years worked there (but in another country B), that this is summed up and I am then eligible for a pension in this state A?

4. What if one hasn’t worked AT ALL in the country you live in when retiring? (EDIT: Apparently there is a minimum-of-1-year duration. If you have less that one year, you have to apply for your pension in another state where you did (?))

5. If I am correct in the assumptions 1-3, how is my pension then calculated in the light of the fact that pensions are calculated differently in different countries? Is this calculated individually per state and then summed up? Or is this somehow "transformed" and adjusted to the system you collect your pension from (i.e. country of residency)?

6. What about the age of retirement? All (?) countries seem to allow you to retire a litte earlier at the cost of x% of your pension. What if one retires in one country at say 65 but would collect a pension in another country only starting from the age of 68?

7. Where are the pensions taxed? Is each one taxed in its origin country separately or is this only taxed in the country one lives in?

8. What happens (tax-wise) when moving your residency to another country after having started collecting your pension?

9. What happens with corporate pension plans? What with private pension plans?