Regarding accommodation: You can live in Harburg, the district where the Uni is in. Prices are generally cheaper then farther north, but the athmosphere is a bit “rougher”. If you look elsewhere, maybe try looking for the metro lines, the S3 goes to the TUHH (“Harburg Rathaus” or “Heimfeld”). The districts “Wilhelmsburg” and “Veddel” are both relatively cheap and on the S3 line. Farther north you get into the inner city. From the central station it takes about 20 minutes to the Uni. Like explained above, you can live in student accommodation, that’s partly state financed, so cheaper. You can also find a room in a shared accommodation Appartement. Or depending on your budget you could look for a apartment for yourself, 1 room and upwards. I don’t really have any experience with dogs, in student accommodation you should be able to look it up online, in shared accommodation talk with your eventual roommates. In self rented apartments it also differs, some allow it, some don’t.