What Billings said in his introductions to The New-England Psalm-Singer, The Singing Master's Assistant and The Continental Harmony about:

sharp (major) vs. flat (minor) keys, and the notes in their scales:
    "In the first place, you must pay great attention to the key note, and the sound if B-mi which constitutes the key note, and causes it to be either flat or sharp; the next principal tone to be regarded, is the third above the key note, which contains a great part of the true air of the tune, for by the sound of the third, we are enabled to tell whether the key is flat or sharp; another principal tone is the sixth above the key note, which is either flat or sharp, according to the key of the tune; for the sixth above A, the natural flat key, contains but eight semitones, viz. from A to F, which is a flat and melancholy sound; whereas the sixth above C, the natural sharp key, contains nine semitones, viz. from C to A, which is very martial and sprightly, and I think is almost as great a mark of distinction as the third: the seventh is likewise a guide in this case, for the seventh above the flat key contains but ten semitones, whereas the seventh above the sharp key contains eleven semitones."  [then: the fourth, fifth, and octave do not differ between sharp and flat keys]
   " ...you may observe in a flat key tune, where the note before the close stands on G-sol, which is a whole tone below the key; but it is so natural to sharp it, that it seems to be doing violence to nature to strike it without the sharp; and I presume all masters of music, both vocal and instrumental, will allow this to be fact..."
[The Continental Harmony-A Commentary on the Preceding Rules]

"Choristers must always remember to set flat keyed tunes to melancoly words, and sharp keyed tunes to cheerful words."

men vs. women's parts
    re men and women both singing the treble or tenor part in 2 octaves: "...in general they are best sung together, viz. if a man sings it as a Medius, and a woman as a Treble, it is in effect as two parts; so likewise, if a man sing a Tenor with a masculine and woman with a feminine voice, the Tenor is as full as two parts, and a tune so sung (although it has but four parts) is in effect the same as six.  Such a conjunction of masculine and feminine voices is beyond expression, sweet and ravishing, and is esteemed by all good judges to be vastly preferable to any instrument whatever, framed by human invention.  [later: but if the part is to be sung in only one octave, it should be by the women rather than the men]
[The Continental Harmony-A Commentary on the Preceding Rules]

"One very essential thing in Music, is to have the parts properly proportioned; and here I think we ought to take a grateful notice, that the Author of Harmony has so curiously constructed our Organs, that there are about three or four deep voices suitable for the Bass to one for the upper parts, which is about the proportion required in the laws of Harmony; for the voices on the Bass should be majestic, deep, and solemn; the tenor, full, bold and manly; the Counter loud, clear and lofty; the Treble soft, shrill, and sonorous..."
[The Singing Master's Assistant-To the several Teachers of Music]

beating time
re Adagio, the slowest mood, each bar containing one Semibreve [whole note] and lasting four seconds:  "...I recommend crotchet beating in this Mood, performed in the following manner, viz. first strike the ends of the fingers, secondly the heel of the hand, then thirdly, raise your hand a little and shut it up, and fourthly, raise your hand still higher and throw it open at the same time.  These motions are called two down and two up, or crotchet [quarter note] beating."

re Largo, 25% faster: "...you may beat this two several ways, either once down and once up, in every Bar, which is called Minim [half note] beating, or twice down and twice up, which is called Crotchet beating; the same way you beat the Adagio.  Where the tune consists chiefly of Minims, I recommend Minim beating; but where it is made up of less Notes, I recommend Crotchet beating..." [in footnote: "When I think it advisable to beat Largo in Minim beating, I write "Minim beating" over the top of the tune, and where these words are not wrote, you may beat Crotcheat [sic] beating."]

re Allegro, twice as fast as Adagio, one second per Minim: "This is performed in Minim beating, viz. one down and one up..."

re 2/4, two crotchets each half a second: "this is performed in Crotchet beating, viz. one down and one up."  [David's Lamentation and Rose of Sharon are in 2/4]

re 6/4, six Crotchets: "three beat down, and three up"

re 6/8, six Quavers: "three beat down, and three up"

re 3/2, three Minims: "two to be beat down, and one up: the motions are made after the following manner, viz.  Let your hand fall, and observe first to strike the ends of your fingers, then secondly the heel of your hand, and thirdly, raise your hand up, which finishes the Bar"

re 3/4, three Crotchets: "two beat down, and one up" (same as 3/2, "only quicker")

re 3/8, three Quavers: "two beat down, and one up" (same as 3/4, "only quicker")

    "....every letter has its own peculiar air, which air is very much hurt if the tune is not rightly pitched; for instance, if a tune is set on A natural, and in pitching the tune, you set it a tone too low, you transpose the key into G, which is perhaps quite different from the intention of the author, and oftentimes very destructive to the harmony, for there is a certain pitch for every tune where it will go smoother and pleasanter than it would on any other letter whatsoever....The best general rule I know of, is, to set the tune on the letter the author has set it, unless he has given directions to the contrary...."
[The Continental Harmony-A Commentary on the Preceding Rules]

    "Great Care should also be taken to Pitch a Tune on or near the Letter it is set, though sometimes it will bear to be set a little above and sometimes a little below the Key, according to the Discretion of the Performer; but I would recommend a Pitch Pipe, which will give the Sound even to the nicety of a half a Tone."
[The New-England Psalm-Singer-Thoughts on MUSIC]

singing [The Singing Master's Assistant-To the several Teachers of Music]
on singing a Slur: "I advise you to take breath just before you get to a Slur; and then you may go through with ease; and I think it is ornamental to sing a Chain of Notes something softer than you do where they are plain."

"Be sure not to force the Sound thro' your Nose; but warble the Notes in your Throat"

"It is also well worth your observation, that the grand contention with us, is, not who shall sing loudest; but who shall sing best.

accenting [The Continental Harmony-A Commentary on the Preceding Rules]
    "...some authors confine the emphatical or accented notes to the first part of the bar, both in common and triple time, and some lay the emphasis on the first and third parts of the bar, in common time, and some others let them fall where they may happen, without any restraint at all; but it is much the best way (I think) to lay the emphasis on the first part of the bar in triple time, and on the first and third parts of the bar in common time, though sometimes it is very difficult for the composer to accent the bars without losing the air, especially in fuging music..."

(The introductions to the three books overlap in part, so that some of the quotes above occur in two or three, but sometimes there are minor editorial differences.)

See also Appendix II, "Performance of William Billings's Music", in David P. McKay and Richard Crawford 1975, William Billing of Boston: Eighteenth-Century Composer, Princeton U. Press.