Hari can we modify the embed extension & build our own embed look with the above-mentioned features?
Go for it. Flarum (and its bundled extensions) are MIT Licensed so just make sure you're maintaining attribution as required.
Understand that Flarum's standards for bundled extensions has to be pretty high, our extensions have to work for general purpose. We do accept PR requests from the public, but the best way to go about it is to start with a discussion here about the scope (plan) of your changes and how you'll accomplish them.
The best way to go about it is probably to fork the embed extension and create your own version with those changes. Then other people can use them and try them out. It doesn't even have to be for a PR back to Flarum's extension, you're always welcome to build extensions that do the same thing as Flarum features/extensions, that's the guiding principle of our ecosystem.