verb/phrase nominalization

Hi. I think it will be easier to ask my question through a few examples.

1a. Hon wo motte kuru no wo wasureta.
1b. Hon wo motte kuru to wasureta.

2a. Kanojo wa yasashii no wo shitte iru.
2b. Kanojo wa yasashii to shitte iru.

And the list continues with other verbs like yakusoku (suru), and the likes of these verbs. Primarily, the question is whether I should use ''no wo''(/koto wo) or ''to'' in these type of sentences. Hope I managed to convey my confusion. Any further example is much appreciated. ^^

1a, 2a, and 2b are correct, but 1b is incorrect.

1a. [Hon wo motte kuru no/koto] wo wasureta. = I forgot [(the act of) bringing a book].

2a. [Kanojo wa yasashii no/koto] wo shitte iru. = I know [(the fact) that she is kind].
2b. [Kanojo wa yasashii] to shitte iru. = I know [that she is kind]./I know her to be kind.

- [Kare wa amerika ni itta] to kiite iru. = I have heard [that he's gone to the US].
- Kare wa [hon wo motte kuru] to itte ita. = He said [that he would bring a book].

"...to" is more for connective "that..." or more like quoting, while "...no/koto" makes the verb into a noun. I'll come back again if/when I come up with better examples.