How can I list the packages I removed on a specific day?
Use this line:
cat /var/log/dpkg.log | grep "2016-05-05" | grep "remove" | grep -v "startup"
And for putting it into a file:
cat /var/log/dpkg.log | grep "2016-05-05" | grep "remove" | grep -V "startup" > removed-files.txt
There are surely multiple and maybe even more elegant ways of doing this, if you point them out I'll add them to my answer here.