Work in deutschland

To work in Germany, you need a nurse certification that is recognised here and German language skills (B2 level or better). If you have that, your chances of finding a job are good, as nurses are in short supply.
Regarding your other questions, unfortunately there are areas with low salary and low cost of living (e.g. Eastern Germany, or the countryside in most areas) and those with high pay and costs (generally Southern Germany and the cities). The nearer you come to Munich, the higher the prices.
Immersion in the culture/locals is possible anywhere, but probably easier in the cities. The weather is cold (at least compared to the Philippines) in the whole of Germany.

Thanks for your reply. How about in northern part of germany?

In Northern Germany, you also have expensive cities (e.g. Hamburg) and cheaper countryside. The weather is more or less the same as in other parts, just slightly more rain and milder winters.

I read somewhere here in the forum that freiburg and breisgau is great city in southern part. Is it really expensive there? What can you say about these cities?

Freiburg im Breisgau is a nice, medium-sized city with a huge student community and a green/alternative flair. Due to it's proximity to (expensive) Switzerland, it is not the cheapest, but probably still better than bigger cities.