Can an annulment be sought if a couple is unsure of the validity of their marriage so that they can remarry each other properly?
No.
For instance, they don’t want a marriage that is merely assumed to be valid or only putative. They want it to actually be valid without any question or doubt. The reason they ask this question is given how easy it seems to get annulments, there is a good chance an extraordinary number of marriages are in fact null, but only assumed to be valid unless proclaimed ‘null from the start’ by the Church. They don’t want their marriage to be only assumed valid. Is that a licit intention?
No, it isn’t a legitimate intention.
Also, is a decree of nullity an infallible pronouncement, or are some valid marriages actually in fact ‘nullified’ or made to be null?
It’s not an “infallible” pronouncement. It’s a legal decision under Church law. Infallible pronouncements are only made in matters of faith and morals, not matters of law. Likewise, a Sacrament cannot be reversed by a legal pronouncement.
Please understand that the Church performs convalidations for the purpose of making a Sacrament of the marriage, rather than merely a human, legal institution. A convalidation usually happens when a couple is married before a judge, protestant minister, rabbi, or someone else; the couple later wants their legal, civil marriage to be a Sacrament, and so the priest “marries them in the eyes of Christ.”
Requesting an annulment of a marriage, just for the sake of later requesting a convalidation would not be an acceptable thing to do. (I’m struggling for the right words here, but suffice to say that it can’t be done.)
As for assuming validity, marriage enjoys the favor of the law. That means that marriage is always assumed to be valid, but the burden of proof lies with one who wants to say that it’s invalid.
If a couple is truly concerned about the validity of their marriage, they should speak with their own pastor. If the first marriage was not performed by a priest (or bishop or deacon) the priest MAY be able to do a convalidation. But if it was performed by a Catholic clergyman, a convalidation is simply not possible (except in very extreme circumstances).