It's fine, nothing about it looks wrong, it looks completely professional.
A little TOO professional. Personally... not as a prospective student... I'd say "lose the stock photography." (I'm 99.9% sure it's stock photography). All it communicates to me is "I want my website to look glitzy." It doesn't help me understand whether you'd be a good teacher for me. In a way, it weakens things by vaguely claiming that your services are good for anything you could possibly use a language for.
"Romance?" Really? You teach attractive young women how to flirt?
Actually... I don't see "me" (retiree) in any of those pictures. Not even Mr. Business. (I hope he's not anyone you know, I dislike that guy on sight).
I think I would put some of the specifics, "I can help you with grammar, vocabulary, pronunciation and preparation for TOEFL and IELTS Examinations" somewhere right there on the front page, and... what is Bagrut? Is that something important that some people might be looking for, that not everyone can teach?
Don't make people click if they don't have to. Try to get as much as possible of what they might to know right there on the home page.
It also seems to me that you've spread a relatively compact body of information over a lot of different menus and links and different places to click. Suppose I to find out if you specifically prepare for the IELTS. Do I click on "Home," "About," "Services" at the top, or "Lessons," "Book a lesson," or "Results" at the left, or "Visit," "Call," or "Contact" at the bottom?
Paddy is right, a domain name is dirt cheap (at least in the U.S.) and if you actually set up the website yourself you can easily buy the domain name and arrange to have it do "web forwarding" to this website.