Yes, the old ones look like they needed replacing - nice looking new ones !
That picture of the new ones loes not show how much clearance you have to the fender.
OK - I guess you did need to stay in that size.
Probably the reason for the tube in the one with the flat is that there was an issue before. Did you see the rims before the new tires were mounted ? I hope there wasn't rust around the bead or you may have a slow leak - I always either check them myself or ask the person mounting to check and use bead seal.