How web programming works from point of view of an iOS developer?

I want to make a website that builds up from similar buiding blocks like my iOS app. What technologies I need? In university we used MySQL + PHP + Smarty + Ajax. and that was pretty flexible. But now after several year iOS programming I see the limitation of it. I.e. it was not object oriented.

In my apps usually I have a local object mapped database based on Core Data. How is it possible create local database in web?

GUI is usually based on tableViews and collectionViews. I know in HTML there is table html element, but what about collectionView? Should I made it also with table / div element?

How can I set up layout constraints in the UI in web? Should I 'hardcode' rules how UI element should behave?

How can I implement segues in web? I need to replace with JS certain nodes in DOM?

What are the cutting edge technologies now in web?