To determine whether these things are valid targets of the spell, they must be included in this portion of the spell description:

The object can be a door, a box, a chest, a set of manacles, a padlock, or another object that contains a mundane or magical means that prevents access. A target that is held shut by a mundane lock or that is stuck or barred becomes unlocked, unstuck, or unbarred.

Notably, "another object that contains a mundane or magical means that prevents access" will be how we determine special cases.

So,

1. knotted rope tying up a PC

Yes. I would argue that a knot that is tying someone's hands together is functionally similar to a set of manacles and the knot could be considered a mundane means of preventing access. So long as there is a single knot because:

If the object has multiple locks only one of them is unlocked.

Locks in this case could extend to knots but you could leave that up to DM discretion.

2. continuous chain without a lock that is holding a chest shut

Yes. This chain is a means of preventing access to the chest. Whether the chain magically falls to the ground or is unlinked without actually breaking the link could be up to DM discretion, but I tend to agree with the other comments suggesting that the spell doesn't actually break an object.

3. buckle holding a belt together

Yes. My first thought on this one was no, but technically the belt prevents access into the trousers. I would argue that the prong on a traditional buckle is close enough to a bar on a door to be a valid target for the spell. To what extent the belt is undone is up to DM discretion.

4. vine/tentacle wrapped around something (either an entry or a PC limb) (considering that manacles are a valid knock target)

Let's break this one up...

For an entry, Yes. If the vines are sufficiently obstructing a doorway to prevent access they could be considered in the same way a barred door prevents access.

For the PC's limbs, No. The reason this is different from manacles or the knotted rope is that there is no mechanism that is actually locked, barred, stuck, or in the rope's case knotted. The reason I said the chain would be valid and this would not is because for the chain to form a loop the last link made would have to be closed essentially sealing the loop. The vine or tentacle doesn't lock or tie itself, and it doesn't produce an enclosed loop.

5. Fingers grasping an object

No. The target must be an object, not a creature

6. heavy hatch covering an escape hole

No. I think there's an important distinction to be made here about the result of casting this spell. Nowhere in the description does it indicate that the target that is being unlocked, unstuck, or unbarred opens. A chest with a locking mechanism will become unlocked and many DMs in this case might describe the chest swinging open as a result, but RAW there is no indication that this is an inherent feature of the spell. The spell description states :

A target that is held shut by a mundane lock or that is stuck or barred becomes unlocked, unstuck, or unbarred.

And

If you choose a target that is held shut with arcane lock, that spell is suppressed for 10 minutes, during which time the target can be opened and shut normally.

Of course for a mechanical lock such as a padlock, it is usually opened due to being unlocked, but the door or chest it is preventing access to wouldn't necessarily swing open as a result.

The spell won't make the hatch swing open, and it also wouldn't make the hatch any lighter.

7. glue/resin sealing a window

Yes. It's a mundane means of preventing access. Knock would definitely unstick the window.

As for the socks, you're out of luck. Unless you tie someone's hands together with them, but in that case remember that Knock would only undo one knot.

Sorry for the wall. I'm open to discuss these if you disagree.