Let's go through this while considering the laws in 1885 when they actually migrated to the United States.
1. The US did not differentiate between European Countries when you migrated. They were specific to whether or not you were solvent financially, and did not care if you said you were from Sweden, or from Germany for that matter. This would not be illegal, even if he had done that.
2. US Immigration records list Friedrich Trump's (later anglicized to Frederick) county of Origin as Germany, not Sweden. He did come from Germany, but it was after he left Bavaria where he was born. Claims that he or his descendants misrepresented his origins as Swedish appear to stem from later statements by Donald Trump about his father Fred (who was born in the Bronx in 1905), not Friedrich himself. These inaccuracies were likely efforts to downplay German heritage amid 20th-century anti-German sentiment (e.g., during World Wars), but they postdate 1885 by decades.
**** A little personal history: Here I will say that my Grandfather changed our last name during the wars to avoid being taken for German, this was something some German folks did back then.
3. There was no federal statute criminalizing inaccuracies on entry manifests until the Immigration Act of 1891 introduced perjury penalties for sworn statements (which weren't routine yet). Even then, enforcement was lax for Europeans, as the focus was on excluding "undesirables" like the ill, paupers, or convicts, not probing origins. Historians note that manifests were often filled out by ship captains or clerks based on verbal reports, with errors common and unpunished.
4. It was not even asked if you ran Brothels, nor was it something that would be illegal for them not to mention.
What Was Asked at Entry?: Inspections were cursory (often 5–10 minutes per person) and didn't probe past employment or moral history for European men. Standard questions centered on employability and public burden risk, not criminal or vice-related activities. Prostitution-related inquiries only emerged in the Page Act of 1875, but it exclusively targeted Asian (primarily Chinese) women suspected of being trafficked for sex work, requiring them to prove they weren't prostitutes. European immigrants faced no such scrutiny; broader exclusions (e.g., for "convicts" or "persons likely to become a public charge") were added in 1891 but didn't retroactively apply or require disclosure of vice operations.
So, in short. Neither of the two things you claim were something that would have been illegal or kept them from migrating even if they were true.