The idea is nice and I really like it, but still there also are advantages of having a separate Link field. Note that I'm not arguing about whether the Remarks field is necessary ;)
However votes are showing that the users are not concerned with this problem - alas, only 4 votes in 3 months..

Right now the tab size is not changeable, sorry. There is however this suggestion on the roadmap: http://roadmap.cintanotes.com/topic/79780-configurable-tab-to-space-autoconversion/ 

Sorry for the delay! Good idea, thanks, added it separately here: http://roadmap.cintanotes.com/topic/114892-browse-button-in-the-link-field/   Please vote!

I love the simplicity of this idea, however there also are some potential problems. I think the concept of the all-purpose remarks field would be more difficult to understand for the new users. Also it will make difficult introduction of additional filters: there will be no more solid information on the URL the note comes from. So for example it won't be easy to build the list of domains (like in browser history). In this way this simplification will be hindering further useful features. What do you think?

I think this is what is meant here: tags which are present in the current view should be displayed differently from tags which are not visible at the moment due to the search filter (just because no notes with these tags happen to be in the filtered list).

Sorry for the delay.
No I envision it a bit differently: you double-click on a tag, not on notes. After that only related tags remain in the list. To go back to the full list, you will have to deselect the initial tag you have double-clicked on, or explicitly switch to "All".

About the hotkey: probably not since Tag sidebar is by design mouse-oriented. Maybe the same behavior should be provided for tag autocomplete, which is keyboard tag interface.