try many other exchanges that are far better than that place. you can try smaller exchanges if you like such as c-cex or cryptopia or bigger ones such as poloniex and bittrex. they all have a proper website, with a decent API and 2FA and a working support and there is not much shady stuff going on in any of them.
but as for your question. i think they changed some stuff about their website, which may be the cause of https going away! i checked it and for some reason it asks me to fill in a captcha to open the site!
and for the 2FA key you only have to contact support and hope they answer you in less than a week.
I stopped using yobit since long ago but because of a certain coin I've logged in and use it again . This explains why my 2fa is disabled even though every accounts I'm using has it enabled . I've contacted their support and unfortunately they didn't give a solution . Here's what I got:
~Snip~
Hope this will help.