#2 makes great sense to me. While it may be true that their home countries have few if any reliable records which makes it difficult to vet those coming here, we have technology that can quickly and painlessly make a completely unique ID of each person so the odds of anyone every coming here a 2nd time without us being able to positively ID them are zero.
There.
Fixed it.
That, of course suggests that DNA samples of every applicant is a mandatory item for admission as a temporary or permanent resident or tourist or visitor.*
In addition, of course to all the personal data currently required.
The inclusion of fraud in any application, as discussed elsewhere, would also trigger permanent forfeiture of any entry into the U.S.A. NO EXCEPTIONS, no Obama-style EOs or even Congressional actions.
The definition of "citizenship" being defined the States as documented in the original Constitution must be also affirmed, and subject only to a Constitutional Amendment.
*A new DNA profile test, which is virtually instantaneous, has been discussed in a recent Freeper thread.
That, together with photo and fingerprint for every visitor, should be in a single database and backed up in a remote supersafe location impervious to hacking.