Does Contact Other Plane allow the contacted entity to be targeted by other spells such as Sending and Dream?

Question

Relevant text from Contact Other Plane:

You mentally contact a demigod, the spirit of a long-dead sage, or some other mysterious entity from another plane. ... you can ask the entity up to five questions. ... The GM answers each question with one word ... [or] might instead offer a short phrase as an answer.

For context, the use of Contact Other Plane will contact a random entity on another plane, per the DM's decision regarding the question below. The caster will know if they are contacting an entity they have previously contacted (not necessarily identity, but more of a "I am talking to Entity Number 3"). Contacted entities are able to lie, and are not omniscient. Given enough castings, a given entity will be contacted multiple times.

Relevant question: How do you decide who will be contacted by Contact Other Plane spell

The spell doesn't really seem to care who chooses or how it's chosen. ...

Relevant text from Sending (emphasis mine):

You send a short message of twenty-five words or less to a creature with which you are familiar. ... recognizes you as the sender if it knows you ... if the target is on a different plane than you, there is a 5 percent chance that the message doesn't arrive.

Relevant text from Dream (emphasis mine):

This spell shapes a creature's dreams. Choose a creature known to you as the target of this spell. The target must be on the same plane of existence as you. Creatures that don't sleep, such as elves, can't be contacted by this spell. ... If the target is asleep, the messenger appears in the target's dreams and can converse with the target as long as it remains asleep, through the duration of the spell.

Relevant text from Scrying (emphasis mine):

You can see and hear a particular creature you choose that is on the same plane of existence as you. ... Familiar (you know the target well) ...

Ignore the requirement for the spell that say the target must be on the same plane as the caster, or otherwise assume that the caster is able to get to the plane of the contacted entity but not necessarily get to that entity (so they can't just talk in person).

Answer 1

Find out from your DM

How this is handled is up to the DM, as by the rules there is neither a clear definition what it means to be familiar with someone that is consistent across spells, nor is it that tightly defined even for the individual spells, nor is it clear that you gain any familiarity by the procedure. The spell merely says:

You mentally contact a demigod, the spirit of a long-dead sage, or some other mysterious entity from another plane. (...paragraph about risk of going insane omitted...)
On a successful save, you can ask the entity up to five questions. You must ask your questions before the spell ends. The GM[sic] answers each question with one word, such as "yes," "no," "maybe," "never," "irrelevant," or "unclear" (if the entity doesn't know the answer to the question). If a one-word answer would be misleading, the GM[sic] might instead offer a short phrase as an answer.

Nothing there states that you see or learn anything about the entity, not even who or what it is. Nor that you'll get the same entity twice. All you get is a handful of one word answers to your questions. The rest is up to the DM.

The text is rather sloppily written, for example it uses the term "the GM", while the term for the person running the game in 5e is Dungeon Master, or DM. Also, it says that the GM answers, not the contacted entity. No wonder you have to make an insanity check.

Your DM already has made a number of calls on the vague corners of this spell, for example, in your setting, the answers can be lies (the spell does not indicate they could), the caster knows what entity they deal with (even if they do not know who it is), etc. What is possible in such an environment nobody here will be able to tell you. You need to find out by exploring in character with your DM.