Snapping isn't a "preset" but a "function". Are you absolutely sure it is off? Also, are you seeing the magnetic timeline doing its thing, rather than snapping? I'm not sure what you're clip is snapping to. A short screen movie would help.
Lines at the top of what? Do you mean the Timecode Ruler at the top of the Timeline? If you see that snapping, then 1- You're zoomed in way too much and are seeing individual frames, 2- You must have clips only a few frames in duration. The ONLY time a clip snaps to the timeline ruler is to each frame, which is determined by the Project's frame rate. Attach a still screenshot of your Timeline. I'm betting we see you super zoomed in.