Can I create a pinterest like website with Drupal?

1.Yes.
2. Yes, with optimization.
3. https://drupal.org/node/2045489

there are quite a few install profiles that mimic pinterest, and themesnap does one that looks quite solid:
http://www.themesnap.com/blog/our-pinboard-pinterest-clone-redesign-plus...

I did using Masonry Jquery plugin on http://biyixia.com/. I think there is no need for a whole new theme. I created a callback using a module and rendered the custom HTML.

It works well except there is just one issue that it breaks the layout if the connection is slow and images are loaded after the Masonry plugin is loaded. I resolved it using the following method:
http://www.qasimzeeshan.com/load-masonry-after-all-the-images-are-loaded/

1, Of course you can. Drupal is a flexible and scalable CMS that can be used to set up any kind of website.
2, This is hard to answer. The speed of a website is determined by several aspects, such as the web hosting (you can search the best Drupal Hosts on Google), the amount of video/audio/image files, the amount of traffic, etc. As to compare them purely for speed, I think WordPress is better due to its light-weight and simple coding.
3, As for theme, Pinterest-design Drupal theme - TB Wall may suit your needs. https://www.drupal.org/node/2045489

1. Yes you can create a website like pinterest
2. Website depends upon hosting and your custom queries. If you write proper code and proper hosting then your site will be running fast. Wordpress or drupal only facilitates the way to do work.
3.https://www.drupal.org/node/2045489