I believe learners may be helped by splitting this lesson into two. In reality more than one noun class is discussed here. Noun classes 11 and 12 cover the singular and plural countable words that are the real U/N class. These include words like uzi/nyuzi, ubavu/mbavu, ulimi/ndimi, etc.
Noun class 14 contains the uncountable and abstract words like uhuru (freedom), uzuri (beauty), and umeme (electricity). These only have one form. Although this class works much like the class 11 singular nouns, it is a different class.
I'd also like to say that this section has quite a few unnatural English constructions, like "I need yarns" or "Rehema needs threads." Most native English speakers would say "I need two skeins of yarn" or "Rehema needs two spools of thread." There is the possibility of "threads" in sentences like "I see two loose threads on your shirt."
I was under the impression, from various resources around the internet, that classes 12 & 13 had merged into other classes in standard Swahili, and that modern U/N was classes 11/10.
Well, I'm not a professional linguist, but as far as I know, class 12 (or XII) is the plural form of class 11. It seems to be pretty irregular though, with lots of initial consonants.
Class 12 has fully merged with class 10 to the point where they're now indistinguishable.
The plural of class 11 is formed fairly regularly by deletion of the u- (or w-) and application of the "N rule".
If deleting the u results in a monosyllabic word, however, it is kept and the N rule applied in front of the U (eg. uso, uzi, ufa do not drop the u and instead pick up ny- at the beginning).
The N rule means an NY in front of any vowel, an N in front of D, J, G and Z, and an M in front of B and V. L and R transform into ND and W transforms into MB. Before the other consonants, the N simply vanishes. All of these are completely regular:
ufa nyufa (monosyllabic, u kept, N applied)
udevu ndevu (u dropped, n applied)
ubavu mbavu (u dropped, m before b)
ulimi ndimi (u dropped, l becomes nd)
ufunguo funguo (... n dropped before f)
ukuta kuta (... n dropped before k)
wimbo nyimbo (w dropped, ny added before vowel)
It looks random, but it's mostly actually quite regular.
In other instances not involving the deletion of a "u", the N rule (such as applied to adjectives) is a little bit different where the stem is monosyllabic - basically it never disappears, so there are words like "nchi" even though the n- would normally disappear before "ch". This is because Swahili dislikes monosyllabic nouns, verbs and adjectives. In words like "nchi" and "mbwa", the N or M is actually the stressed syllable.