The Invisible condition applies only to the invisible creature itself.
The rules language in the Invisible condition (and similarly the Invisibility spell) indicate that only the invisible creature itself is invisible, not other creatures affected by the creature.
From the Invisible condition:
While invisible, you can't be seen. You're undetected to everyone.
There's no indication that other creatures are also affected by the invisibility, unless the effect is making those creatures have the Invisible condition as well (ex. both are behind an Invisibility Curtain).
With this context, here are the answers to the questions (in order). The first two questions have clear answers in the rules:
- A huge invisible creature doesn't make creatures behind it invisible. They would provide Standard cover to the creature behind them (see Cover rules). As a GM, I would rule that if the Huge creature's cover bonus is the sole reason that an attack was a failure, and the Huge creature was Undetected, they'd become Hidden instead of Undetected. However, there's no clear rules interaction for this particular case.
- A tiny creature occupying the same space as a Huge invisible creature is still visible. The tiny creature would have Standard cover.
The final two questions do not have clear answers, and would require a GM ruling:
- Unless the Huge creature is using Swallow Whole, there's no rules text regarding one creature hiding in another creature's mouth. This could perhaps be ruled as using the Take Cover action if it's hostile or indifferent, or perhaps riding (see "Riding PCs" text) the larger creature if it's friendly. While I would rule that the tiny creature is invisible in this case (in a manner similar to the invisible creature's equipment being invisible), this would require an individual GM ruling.
- As with the previous question, there's no clear rules for this interaction. If both parties are Friendly to each other and agree to this plan, the clearest ruling would be to treat this as the tiny creature riding the huge creature, meaning both creatures would lose one of their actions each turn. If the tiny creature is attempting this maneuver with a Hostile huge creature, the tiny creature would effectively be inflicting the Grabbed condition on themselves.