Hello, to make a backup of your contacts go to Settings> Accounts> Google> here you you click on your Google Account you use typically> touch on "Contacts" and you a circular with two arrows rotating icon appears, once finished turning and removes the icon, you'll see that "last sync said at ...... (time and date) and ready.
And another thing, you say that you appear "updating the list of contacts," Maybe it's the 2000 contacts, Proba this: lets you load or refresh the list ...
Another (and do not think that has to do) Clean Master ProBa to download and click on "junk files" and see what takes these 4GB (cache, some rare archive ...).
If it did not work any of the above stores all your data, contacts, important things and restore it to factory settings (you have left your phone as if you had purchased recently).
If not ... I have no idea that it may be ...
I hope your problem is solved