In my experience with Kobo's software, no. Granted, that may have changed in recent updates. KOReader does allow you to remove the header and footer. (Indeed, the header is disabled by default.)

One option is to use the manual factory reset. Kobo's eInk based readers have a separate backup partition which contains a backup of the firmware. It performs a recovery by reformatting the system and user partitions, then decompressing the factory firmware and database files onto the system and user partitions respectively. This is effective since KOReader nor Kobo Start Menu do not touch the backup partitions. I'll let other people speak to the Aura's compatibility with this software since I have only used it on the Aura HD and Aura H2O.

(1) Yes. By default KOReader shows a tiny footer that shows the progress. You tap on the footer to cycle through the various display options, one of which disables it. It is actually so small that you may prefer to leave the footer in place since it does not alter the amount of text displayed, and would only amount to about one line of text at the smallest font size if it did free up that space. (You can also choose to add an optional header, which is also considerably smaller than Kobo's counterpart.)

(2) Yes. The most reliable option appears to be using locally installed stardict dictionaries. You can have several dictionaries installed, and switch between them. You can also do searches of Wikipedia with an active wifi connection, but it is very limited (which is why I started with the stardict suggestion). It only displays part of the article, and does not support links for disambiguations.