They are the original wheels in that last pic. The tires and axles (12L straight through is easier for me) came from the Technic Police Interceptor pull-back because I had it already and didn't mind taking the parts.
I designed it only using parts I had on hand, but it is still pretty sturdy as I was careful to address weak areas. Obviously the original design was pretty much locked together because as you see you have to tear it down to the frame to even remove the old axles. It's not quite as "connected" as that because I replaced some of the technic-pin connections with regular plates/bricks, but I can still easily pick it up, roll it around, etc without anything coming loose. If I had a few black 2x6 plates I would change the very bottom where I used a grey 6x6 plate as I think it would look better when you flip the car over, but that's not really a big deal.
The front is a little weaker. It will come apart if you pull down on the wheels/axle, but again it's fine with general handling of the model. I had all the wheels installed as I was rebuilding it last night and nothing came lose during that process either.