How do I apply for pension in another country?

You should send your application to the pension authority in the country where you live.

I live in Finland and is elderly pensioner since some time. My daughter lives in Sweden and I have also considered moving there. What about the pension, if I move to another country?

Retirement pensions are paid to you regardless of which EU or EEA country you live or are staying. It is neither being reduced or suspended or altered in any other way. So if you move to Sweden, your pension is paid to you to Sweden.

I am a nurse and living and working in Denmark. I have been offered a substitute in 14 days in a hospital in Norway, and would like to take this during my vacation. Should I pay social security contributions to Norway?
When you work for a Danish employer in Denmark and a Norwegian employers in Norway, you are covered by the Danish law when you live in Denmark. Fees should therefore be paid only in Denmark. You need the form PDU1DK that you can use as documentation of the Norwegian authorities.
What must I do to get unemployment benefits in a Nordic country?

When you take a job in Finland, Sweden or Denmark, you must sign up for an  unemployment benefit fund to get the right to compensation for your income losses. In Norway, Iceland, Greenland and the Faroe Islands, you will automatically be covered by unemployment insurance.