Traveling from Poland to other European countries while waiting for karta pobytu

Hi, I am now living in Krakow. I am now waiting for Karta pobytu. but I want to travel to Germany and Spain.
So, my question is:

Is it possible for me to travel to other Schengen countries with only my passport？.
Should I ask to Polish Border Guard？

My current status:
I came to Poland on Sep 22 and had the stamp on passport in the airport.
I submitted the documents in immigration office for Karta pobytu and received the red stamp on passport on October 17.
My nationality is Japan (we can legally stay in the country without visa for 90 days)
I am now university student.
I will travel to Germany and Spain by bus on December(first week).

Yes, Japanese tourists can visit any given Schengen area country within their 90 days visa-free stay.

Legally* you'll have to leave Schengen zone on 15 January 2019 and within those 90 days you can travel anywhere you want.

You can also do it from Spain if you want. You don't have to travel back to Poland to legally leave the EU.

* I said legally since Germany and also Spain have now more trouble than tracing one Japanese tourist who may have extended his stay. Millions of North Africans without papers are waiting there to get their "refugee status". Poland would be more strict on keeping the date.