These are my two cents, they probably add too little to previous postings.
Congratulations on your the new cookware. Looks really great in that rack, keep it there so you use it often.
As Robo410 indicated, most nicks and scratches are from handling. I am sure that TJM or homesense buy lots of seconds; but in good condition cookware, that sell at a discount price. The price you paid for the set is what a Mauviel frying pan costs in USA approx.
Relative to your questions:
1.- If you are planning to use the 1 mm pans daily, be prepare to care for them.
There is nothing wrong with them, but they will require retinning sooner than a thicker pan and they will be more susceptible to damage than the heavy ones. Watch out for the burner temperature when using them !
2.- The scratches in the edge or the outside should not affect performance.
The inner scratch doesn't seem to be significant and looks like it affects the bigger pan (the one to the right on the picture). If you are not going to use this pan often and fully loaded, I would not worry so much. I personally like to be in the safe side and would look for a replacement pan in another store.
3.- The gouge in the bigger pan should not be an issue, specially if it is on the side wall.
The hammered wall has higher mechanical strenght relative to a smooth wall.
4.- You can get rid of the sharp edges with sandpaper as suggested or run the dull side of a SS object like scissors at an angle, this will remove some of the sharp edges. Don't forget to clean the pan afterwards to get rid of the shavings.
Stainless Steel is nickel plated, Copper is retinned. Look for the appropiate shop to perform this work and ask them to check the gauge in the bigger pan.
I have some Baumalu pans and don't use metal utensils, I use wooden spoons and silicone coated whiskers. I have gas burners and rarely use high heat with cooper pans, they are very efficient.
To clean them, I just spread some table salt on a salad dish, drop lemon juice on a sponge, dip it on the salt and then rub it on the pan. After that, I wash and towel dry the pan promptly.
Again, congratulation on your new cookware.
"Tell me what you eat, and I will tell you what you are" Anthelme Brillat-Savarin