mpeg2 is not the best editing format unfortunately. Any chance you can go back to the original source footage? Was it a Premiere project that created the mpeg2 file you have?
If not then you'll want to convert the mpeg2 file to a better file type. I've not done this soothers here will give you the best advice on exactly how you might do this.
But once you have an editable format the job is easy in Premiere. In fact, your hardest job is creating the logo in the first place. You can either use Premiere title app whcih integrates seamlessly or if your logo is complicated then create it in your favourite drawing package (Photoshop. Paint Shop Pro, etc). Make sure you save it with a transparent background and tothe same dimensiosn as the video you are editing. Import into Premiere and simply place the graphic on a layer above the footage you want. Done!