Rust sucks! As far as stitch welding you will be fine. There is really no structural integrity gained by welding the whole length in your case. When welding thinner materials I try to weld fit grind fit to ensure my fit is right. When grinding, whether using a grinder, end grinder, or dremmel, be Leary of flap wheels and tiger paws. They are excellent tools to complete the job and tend to give you a smoother finish, however, they also flex. This flex will cause you to take away material on the edges of your weld making the area adjacent thinner. Take your time but you don't have to be anal. Everything looks great so far. Also, if you blow a hole while welding just get a piece of brass or copper and use it as backing then weld the hole up. You can grind to smooth it out. If you don't have a piece of 1/2" copper I would recommend getting one. I have one that is approximately 3"x6" for instances like that. It comes in handy.
Also remember, no matter the level of the welder we all have to grind and make repairs at times. Don't get to frustrated when you have an issue. It's just metal and can be repaired. We hardly ever throw a piece of metal away. We repair it and keep going. As an inspector I think I am one of the most hated guys on site because welders hate grinders but I make them use them all the time.