To answer your question: widow cannot mean never-married. By definition, a widow is a woman who has been married and her husband is dead.
Not sure that is your question though. Your presentation is difficult to follow. I am just answering your question in your heading.
Every since antiquity, centuries before the present passage, χήρα has meant "widow", a woman bereft of her husband. This goes back to Homer and the Iliad (LSJ Greek Dictionary).
The case where it is used metaphorically is when it designates a dish of food that is "widowed", that is "without sauce."
There is nothing in 1 Ti 5:3ff that would suggest anything other than "widow.". In verse 3 the "real" widows should be respected (χήρας τίμα τὰς ὄντως χήρας) in contrast to other widows who have children or offspring who should do their duties and take care of them (verse 4).
In verse 9 it is a question of older widows (not under 60) contra younger ones (11-14) who, the latter, are recommended to remarry, have children, take care of a home.
Unfortunately I can find no hint of χήρα being ambiguous. The English translation "widow" fits in all cases.
Somewhat related. There are cases where a "widow" (χήρα) could be called a παρθένος, a "virgin":
Clement of Alexandria Stromateis VII 72,2
ὁ γὰρ ἐπιθυμήσας καὶ κατασχὼν ἑαυτοῦ, καθάπερ καὶ ἡ χήρα διὰ σωφροσύνης αὖθις παρθένος. (Something like: he who felt desire and controls himself, just like even the widow, through self-control, becomes a virgin again.)
But that is the other way around from what you are asking. It is a case of a formerly married, now widow, attaining virginity again.
There is a very good discussion on this in J. B. Lightfoot's comment to Ignatius' letter to the Smyrnaens 13:
ἀσπάζομαι τοὺς οἴκους τῶν ἀδελφῶν μου σὺν γυναιξὶν καὶ τέκνοις, καὶ παρθένους τὰς λεγομένας χήρας.
(Something like: I greet the homes of my brothers together with their women and children, and the virgins called widows.)
J.B. Lightfoot's explanatory translation/paraphrase is:
I salute those women whom, though by name and outward condition they are widows, I prefer to call virgins.
I was asked to adress "first faith".
@Geremia I do not read this as "first faith", but "important oath."
What we have to do with here are the various organisations within the congregation. Deacons and deaconesses in chapter 3 (among other positions).
One of the organizations was the order of the widows. The widows were enrolled (1 Ti 5,9: καταλεγέσθω) and it would be natural that acceptance into an "order" was accompanied by an oath (τὴν πρώτην πίστιν).
Now these young ones risk getting that loving feeling, alienating them from Christ (5,11) breaking their pledge, that they made when joining the order. It is therefore better that they get married again instead of burdening the congregation's resources. (5:14, 16)
Besides, they are young, busybodies who loaf around and gossip, instead of earning their support from the congregation by offering services in return (taking care of orphans, visiting prisons etc).
This was a costly order for the congregation and should ideally be limited to "real widows" (widows with no means of private support). So if one of the members had a widow in their family, they should take care of them so that the congregation's resources would be enough for the "real widows." (5:16)