No, that's not how markets work.
1080 ti's have stopped being manufactured. Therefore, the supply decreases while the demand increases, leading to prices rising.
The 2000 cards will not affect the prices of the 1080 and 1080 ti's. In a normal market, where 1080s were still being produced, yes, the price would drop.
Those won't go down, manufacturers aren't making 1080 ti's anymore.
If you're gonna upgrade your build you should go with Ryzen, much better longevity. AMD said that Zen will be supported til' 2020 I think, gonna have to look that one up. The cheapest APU for Zen is the 2200G, and according to UserBenchmark, the 8100 is only 3% faster than the 2200G, and that's not even taking into account that you can overclock the 2200G at $30 less unlike the 8100. So if you were looking to upgrade, I'd give this list that I made a look: https://pcpartpicker.com/list/wvwRMZ
570 is also a lot better than the 1050 ti, and I can buy one for the same price as the 1050 ti. Just look up some benchmarks. Also if you wanna get a better case, the Cougar MX330 from the 8100 build is still a good choice.
How much would this be in U.S. dollars?