I don't know why, perhaps it's in the works. Not all websites have apps for smartphones...

Your question is not very clear

What do you mean? If you refer to the toolbar on the lower right corner of the window, please turn on the "chat" button on the top.

Hey guys. This is Sam from italki support staff. https://itunes.apple.com/us/app/italki-messenger/id569299238?mt=8 We've actually just released an italki app, but its still in testing, download it and write a good review on the itunes site.

It's clear. I also would love an app for iPhone or android (though I have an iPhone, so feel free to release that first :)...) I spend a lot of time on my phone and the site is kind of clunky in a mobile device, and An app would help smooth that out and I wouldn't feel like I had to wait til I was home to read/send messages.