1) As far as I can tell, you cannot just search the web from inside the book. There is a box with one tab for the dictionary definition, and one tab for wikipedia that shows up when you highlight a word (
see this pic from amazon). You can also translate from the more menu there. ETA: if you're asking about the "search" button on the lower left, the options there are: this book, all text, and kindle store. Internet is not an option.
2) Yes, you can continuously flip pages by pressing and holding the arrows in the page flip window.
3) It seems to depend on the file size and whether it needs to be converted. It usually takes about a minute for me, sometimes a bit longer, but I've never had it take over five.
4) I don't have experience with the android app, but to get cover art on your books on your PW, you will want to add books through Calibre ("send to device"). You can also get rid of the Personal banner via this method. Cover art is not fetched from Amazon. Amazon uses the ASIN to fetch information, and Calibre fills in a random ASIN when it processes the file. Something about Amazon not liking their data used in that way from sideloaded books? Anyway, no. Not fetching from Amazon. You'll need to make sure your cover is correct in Calibre.
5) This does happen, but you can go back and delete the highlight from your notes/highlights, and the note will remain.
6) No experience here, sorry.
7) No experience here, as I don't have a 3G kindle. However, since I don't, mine is only
name@kindle.com. Only one copy shows up in the cloud, and I don't get confirmation emails.
8) You can convert to azw if you like (this will allow you to embed custom fonts, for instance), but be aware that Amazon does not support sending azw/azw3 format files through their send to kindle service. If this is your intent, stick with mobi.
9) If you download the send to kindle app onto your computer, you may checkmark multiple devices to send the document to. Otherwise, I believe you are correct.