DOES immigration officers have access to bank statements?

I recommend that you speak with an immigration attorney immediately about this and how it relates to your individual case before filing any document with USICS. In answer to your question, usually not, but if one are indicted or investigated for a crime then police can look at their bank statements and records. If an immigration officer becomes suspicious, under certain circumstances, he may issue a request for evidence and ask for the bank statements, and if the applicant or petitioner does not submit them then the the application or petition, may under certain circumstances be denied. Again I highly recommend that you speak with a well qualified immigration attorney before filing any document with USCIS.

No immigration officers do not have access to your bank statements unless you provide them.

They can if they feel there is fraud. They can refer the case to FDNS or ICE who can obtain a subpoena for the records. CIS can use any online database or social media as well to either impeach you or corroborate your story.