There are four main GSM providers (Orange, Play, Plus and T-Mobile) and each of them offers very good network coverage throughout the whole country. Pre-paid SIM cards can be bought easily without any documents required. All GSM operators also provide mobile internet access. When bringing your phone to use with Polish SIM card, please make sure your phone is not vendor-locked ("simlocked").
They are no critical security dangers, a general caution is advised like in many western cities. Emergency phone is 112, both from mobile phones and landlines. Law enforcement is performed by Police ("Policja") and in the bigger cities additionally by Municipal Guard ("Straż miejska"). Medical rescue service is called "Pogotowie ratunkowe". Fire-fighters are called "Straż pożarna". They also deal with non-fire technical emergencies.
Please make sure you have Health and Travel Insurance valid within the territories of Poland, Czech Republic and Germany as well as any other country you would be travelling through.