Hi Sriram,
Good to hear of your interest in TiddlyWiki5, and glad you were able to try it out.
The documentation is a little dishevelled at the moment which is why some of the results of your experiments seem a little unexpected.
1) This should have worked in the same way as (3) below, I'm not sure why you got different results
2) If you are familiar with Chrome developer tools, or equivalent, it would be illuminating to report on the network HTTP issued when the failed save occurs
3) This is the expected result. The approach of downloading your changes out of TiddlyWiki, rather than saving them directly, is necessitated by modern browsers ongoing suppression of the saving features we've used in the past. Although the 'download' thing takes a bit of getting used to it's pretty cool that it works on virtually all desktop browsers. For many people the ability to save changes whilst offline is a lifeline that they need to use now and again, rather than something they do regularly. For those people that need to work offline regularly, there's options like TiddlyFox and AppJS.
4) That is correct,
dropbox.tiddlywiki.com is only for working with old 2.x TiddlyWiki documents. TiddlyWiki5 will work with Dropbox (and similar) directly.
Best wishes
Jeremy