Thanks for the link Astro14 but over here there is no one as professional as them. I went to another rim repair business, in this one at least they looked like they knew what they were doing, but they quoted me at least $200 USD to make the repairs, it could be more depending on how the repairs progressed.
I didn't want to keep throwing good money after bad, and the junkyard option, suggested by zzyzzx, is out of the table as it would surely be stolen parts.
So I went to the dealership to buy a new rim, it really surprised me that in two days they gave me my new rim. I picked up the new rim on Wednesday, it cost $285 USD and I got the new tyre at a local Continental garage for $185 USD.
The new tyre is the same size, with the same pattern, load and speed rating and also is made in the Czech Republic as the factory ones, the only difference is that the originals are ContiPremiumContact 2e and the new one doesn't have the "e".
So, hopefully here ends the tale of the open manhole, we'll not quite I still have to take the car to get an alignment, probably tomorrow, I destroyed the old rim and tyre so no one can use them. I tried to make the parrot thingy with the old tyre but it was really hard to cut through the steel belts and to turn it inside out. I did manage to get the basic shape but I lost my patience and gave up. Here are some pics.
