Kid as young goat is from the 1200s with
Extended meaning of "child" first
recorded as slang 1590s, established
in informal usage by 1840s.
Dictionary.com defines kid as (informal) child.
You would use it in direct conversation with persons you know well
"Does your kid collect stamps?"
although I don't see it as too informal to ask someone, "Any kids?" instead of, "Any children?"
This use of next Tuesday to mean Tuesday of next week is fairly old, according to the Oxford English Dictionary. They include examples under the definition:
Applied (without preceding the) to days of the week, with either the current day or (in later use; orig. Sc.) the current week as the implicit point of reference.
Thus (for example) next Friday may mean ‘the soonest Friday after today’ or ‘the Friday of the coming week’. The latter may be indicated contextually, e.g. by contrast with this, but it is not always clear which meaning is intended
a1592 R. Greene Frier Bacon (1594) sig. B, Thou knowst next friday is S. Iames, And then the country flockes to Harlston faire.
So the use of next --day came after 1592. However, there is another use of next with a weekday that predates this:
c1390 Chaucer Miller's Tale 3518 Now a Monday next, at quarter nyght, Shal falle a reyn.
There is also this:
c1230 (1200) Ancrene Riwle (Corpus Cambr.) (1962) 211 Ȝef‥ȝe ne beon nawt ihuslet i þeose isette tearmes, beoð hit þe neste [a1250 Nero nexte] sunne dei.
Having traced back the references in the OED, it is possible that the form next --day is a fairly original structure. Next has been used to mean "Designating the time, season, etc., following directly after one described, spoken of, etc." in both early and late Old English.
The OED does note that next with a weekday is:
Applied (without preceding the) to days of the week, with either the current day or (in later use; orig. Sc.) the current week as the implicit point of reference.
So next Tuesday originally meant the Tuesday after whatever day today is, but there is no clear notation of when the additional meaning was added. The use of Tuesday after this current week was noted in the OED as being used by 1711.
Best Answer
In the eighteenth century, the overwhelming majority of matches for "am/is/are/was/were terribly" link to words such as afraid, alarmed, broken, bruised, burnt, frightened, hurt, injured, maimed, mangled, oppressed, shaken, shocked, and wounded. All of these phrases suggest severe physical or psychological damage—and just cause, one might say, for terror.
But at some point in the late 1700s, a different sense of terribly begins to appear. It wasn't that terribly in many of the instances couldn't be interpreted as meaning "very badly" (in a figurative sense); it was that it could just as plausibly be interpreted as meaning "extremely" or "very"—with no necessary grounding in physical pain, mental suffering, or terror.
The Sydney trove
In my Elephind searches of U.S. and Australian newspaper archives, the earliest matches for this new sense of terribly emerge in the 1820s and 1830s in a specific locale: Sydney, Australia. Five such examples appear in city newspapers during the years from 1824 to 1832, a period when the usage was not present in Elephind matches for terribly from any other U.S. or Australian newspaper.
From a letter to the editor of the Sydney Gazette and New South Wales Advertiser (November 18, 1824):
From "English News," in the Sydney Gazette and New South Wales Advertiser (May 9, 1829):
From "New Views of New South Wales," in the [Sydney, New South Wales] Australian (April 28, 1830):
From "Circumstantial Evidence," in the Sydney Gazette and New South Wales Advertiser (July 14, 1832):
From "American Expressions" in the Sydney Gazette and New South Wales Advertiser (November 15, 1832):
This phenomenon isn't limited to terribly. For example, from the "New Holland" in the Sydney Gazette and New South Wales Advertiser (September 26, 1829):
And from "Latest English News," in the Sydney [New South Wales] Monitor (February 1, 1832):
English antecedents
The emergence of terribly in the sense of "extremely" in Sydney suggests that the practice may actually have started in the British Isles, a possibility strengthened by the fact that the earliest (1824) Sydney match is from a letter writer who reports having been transported to the colony as a prisoner around 1810. I don't have a subscription to the British Newspaper archive, so I can't see the original images of the newspapers there, but I searched through the thumbnail matches for "were terribly" and found a number of early instances in which terribly appears to be being used in the figurative sense of "extremely." (In these examples I have corrected what appear to be OCR errors, when the actual word used seems obvious.)
From Saunders's News-Letter (August 14, 1778):
From the Northampton Mercury (August 5, 1782):
From an account of a boxing match in the Leeds Intelligencer (June 17, 1788):
From the Kentish Gazette (December 9, 1791):
From the Hereford Journal (July 16, 1794):
From the Derby Mercury (September 25, 1795):
From the Northampton Mercury (October 10, 1812):
From the Suffolk Chronicle (March 18, 1815):
From the Hereford Journal (August 13, 1817):
From the Hereford Journal (August 13, 1817) (very likely the same article responsible for the preceding excerpt):
From the [London] Morning Advertiser (November 5, 1819):
From the Hampshire Telegraph (August 10, 1829):
From the [London] Morning Advertiser (September 8, 1829):
Conclusions
Until fairly late in the eighteenth century, terribly seems to have been limited to instances involving extreme physical or mental suffering. The first movement (by 1778) beyond that narrow usage seems to have involved mental states—from terribly alarmed, frightened, shocked, and afraid (all of which contain an element of panic) to terribly disappointed and terribly chagrined (which suggest serious unhappiness but not terror). By 1788, instances had begun to appear in which terribly meant "badly," with a clear sense of harm or dire threat: terribly taken in, terribly punctual [threats], terribly rent [clothing].
Next (by 1791) came the introduction of terribly in a figurative sense of "badly" that became indistinguishable from "extremely": terribly disappointed that a hoped-for celebrity sighting failed to occur; terribly mistaken about some objective point of fact that carried no dire consequences; terribly out of the way geographically.
And finally came the appearance of terribly in settings where the word means "very" or "extremely" but can't mean "badly," as in the 1817 observation of how "terrible funny" it is to hear people speaking another language and not be able to understand anyone. Other instances of this positive use of terribly appear at various points during the 1800s: terribly glad (by 1842); terribly sweet (by 1843); terribly good (by 1849); terribly wise (by 1849); terribly thoughtful (by 1850); terribly amusing (by 1851); terribly devoted (by 1851); terribly virtuous (by 1856); terribly loyal (by 1863); terribly comfortable (by 1865); terribly polite (by 1866); terribly kind (by 1867); terribly happy (by 1875); terribly generous (by 1886); terribly courteous (by 1889); and terribly friendly (by 1895).
It's interesting that the 1819 instances of terribly used in a non-negative sense ("terrible sharp [meaning 'having a good wit']" and "terrible funny") involve an uneducated speaker who uses terrible, rather than terribly, as his intensifier of choice. The bumpkin element in the origin of this usage is underscored in this slightly patronizing instance from the Salisbury and Winchester Journal (November 18, 1839):
Also noteworthy is a strong hint of sarcasm in the wording of the 1829 instance ("terribly moral"), as if to signal that the author recognized the incongruousness of juxtaposing terribly with moral. But over time, as often happens in English, the upper classes adapted themselves to the uncouth provincial expression and came to use it with no more self-consciousness than the nearest yahoo would in saying the same thing.