Czestochowa, first are you British?
Sorry just checked your profile and you are. As Poland is part of the EU now you do not have to leave when three months is up.
Will I encounter problems applying for the Residency card with no "official" payslip from any company/accountant etc just a print out of a bank statement.
Simple go self-employed, there are great deals to had being self-employed at the moment, for example your social security payments will be 50% for 2 years, which then entities you to health care and a pension. It is quite easy to set up you will need a Polish friend to help though. And find yourself a good accountant paying 60zl per month is nothing to what they can save you. When you have all the details or even part of the details then it will be easy to provide them with the evidence they want. And in addition to this I save on average about 15% more on my salary each month.
Be careful with this because at the moment there is no decision on whether we need this or not. I have been here for seven years now and I need a new card because it has run out, but I went to the office the other day and they told me that I cannot get a new card yet as the old one's are obsolete now and there will be no decision what to do until after the election. No doubt Polish offices being what they are will tell you different, but I checked it out with Warsaw and it is true.