We have already seen transactions as high as those high peak days, we have seen the second biggest day in bitcoin transaction history, nothing happened at all. Which means people are already buying bitcoin like crazy and they are sending/receiving bitcoin like crazy without any problems at all.
Sometimes it changes the time period which makes transactions take a bit longer than usual but the fee doesn't change at all. Thanks to developments in stuff like segwit and then lightning network the transactions are now cheaper and they are even faster as well which makes it super easy to do all of this. So no, even if bitcoin goes to a million dollars each (lol I wish) there won't be a problem because we do not have a static blockchain, we have a dynamic blockchain that runs equally no matter how small or big it gets.
Sorry, but thats just plain wrong. The fees have already started going up recently, and we're at the very beginning of the bull run! The fees are going to be monstrous once the market really gets hot in the next year or two. Segwit will help some, but by some I mean a very little amount compared to the onslaught of transactions that will come as the market gets hot again. Even if segwit adoption were at 100%, and right now its only at like 40% I think, it would still only very slightly alleviate the fees as segwit only roughly doubles the amount of transactions that can be handled. That's not much when tens of millions, or maybe even hundreds of millions, of people start pouring into crypto.