Many thanks for this, Mme.
It's beautiful.

The mode I melody, Chrste redemptor, the hymn at vespers of Christmas eve, is one of my favourites. It appears at no. 485 in The Hymnal 1940 with a translation of Jesu dulcedo cordium ('Jesu, Thou Joy of Loving Hearts'), which is yet another cento of Jesu dulcis memoria. The 1940's version of this tune is the slightly more elaborate Sarum one.

Whoever told you that must have had very little experience.
i can just imagine that the he or she who told you that spoke in a decidedly definitive and authoritative tone which presumed a non-existent expertise.
I have known many people quite a bit over 35 who could sing as beautifully as some in their prime - including some professionals.

I am 'a few' years over 35 and can sing as well as ever. The only toll age has taken on me is my ability to sing countertenor - that, and failing breath capacity. I've always been, and still am, adept at both tenor and bass, and used to sing countertenor as well - but the latter is gone now.

I have had a number of people who were quite old who were the backbone of sections in some of my choirs. I must admit, though, that I have known of some few who should have stopped singing in choir (but not necessarily in the congregation) long, long ago. Then there are those, n'est ce pas?, who, though young and under 35, have no business being in choir.

Then, there is that unusual class of persons whom one encounters only rarely, who really cannot sing but absolutely love being in a choir, become devoted to it, will do anything for it, and are never ever absent from rehearsals or masses. Most have to be weeded out with kindness. A few make no noise at all, do no harm, and are sometimes warmly tolerated.

The most stunning example in the opera world was Alfredo Kraus, who sang professionally right until his death thanks to his absolutely exquisite technique, perhaps surpassing all his contemporaries in that regard.

This is purely anecdotal, but the technique I’ve observed to suffer the most with age is straight tone soprano (in imitation of the Boychoir sound). It’s frequently easy for young women to do, but if it’s not informed by a lot of technique, begins to get unattractive in middle age.

One should sing as long as he can sing.
And when he can sing no more he should sing in the shower.
And when he can do that no more he must sing in his heart

Since there are a large number of techniques necessary for fine singing, a variety of exercises are usually called for.
However, most famous singing teachers are nearly unanimous in recommending running scales in order to train matching tone across vocal registers and breath control. Things like: 1234-5432-1234-5432-12345678-987654321.

That’s a huge blanket statement

What I’ve observed is that the analytical and the non-analytical teachers produce roughly equal results among students. The kids that could sing well get better at it, the kids who couldn’t, don’t.

Also, what is a falsetto exercise is and how it’s good for everyone since women don’t have a falsetto register?

When I was at a parish in Houston, we had a singer that had sung in the parish choir for 50 years. Just think about that. She had sung and knew practically every common anthem in the repertoire. I would often come up with some obscure piece, and as soon as we started rehearsing it, she would say, ah, yes, I know this...
We presented he during her fiftieth year, a bronze pope Benedict medal and some gifts. There really ought to be a way to honor long time choir members.