Hello Tamar!
I think it would be good for you to create your website locally on your computer using maybe mamp https://www.mamp.info
You could also create your new website on a subdomain of your current website like new.tamarbd.com
Maybe that is easier.
You would have to insert all of your content of the current website into the lay theme website by hand. For example you would need to create projects and put your images inside.
When your new lay theme website is finished, you would need to move that website to tamarbd.com.
I wrote a little explanation here about how to move a lay theme website: http://laytheme.com/documentation.html#moving-website
This may be a bit hard to do if you haven't moved a website before and I was thinking to create a video tutorial about that one day.
If you want to recreate your website so that it looks the same as right now, I think maybe lay theme would not be the right choice. There is no built in support for a menu that has sections like your menu for example.
If you like I can send you a test account login so you can try the theme a bit and then you can make your decision if you want to buy it.