For "Country of residence", the trick is to type the first three letters of the country name, eg gre for Great Britain produces a pop-up with a few county names that includes Great Britain; uni for United Kingdom gives a list that is too short to include that name, but continue trying and unit brings up the list that includes United Kingdom.
Of course, if I happen to know the ISO three-letter country code, eg SWI for Switzerland or GBR for Great Britain, this is the most direct way to fill in the field for the country of residence. (Lower-case letters are also accepted for the codes)