Hi Miguel, such a huge leap from v2.1 to 3.7 is asking for trouble. There have been so many upgrades to Moodle and its plugins that the courses are not likely to survive. You really only have two options, one is to step through the upgrade process, about 3 version steps each upgrade, but that too can get you into trouble if you are not careful. That is, from v2.1 go to v2.4 then v2.7 then v3.0 then v3.3, v3.6, but you may find that going from v2.7 to 3.0 needs to stop at v2.9 along the way. The other option is to rebuild everything from the ground up, but that too has its downside. If you are not familiar with the changes to v3.7 then it might be a seriously frustrating option. Others have experience and may offer different impressions and advice, but whatever you do, make sure you do not decommission your existing site until the new one is completely ready.
As for the quiz problem, you can replicate the quizzes in another course, with slightly different long and short names and course numbers, enroll students in the respective courses and redo the quizzes that way. You may also reset the course, which removes all user data and un-enrolls students, so you have to re-enrol them anyway. I suggest you archive the existing courses, import them to a new Category pointing your links to the imported courses, reset them and that should get around the limitation, it might not, but it should.