I have searched as hard as I am willing but have not been able to find a definitive answer to the question: does a creature having the natural ability of telepathic communication (not provided by a spell or magic item) have the ability to communicate with any creature that has a mind, or must they know the same language as that creature? I have found some reference to being able to impart the general meaning of a subject, through the use of shared imagery, but I'm still not sure if a creature (like a slaad, for example) who does not know the common tongue, could effectively communicate telepathically with a human. If it is only through imagery and the like, how does a polymorphed slaad sew discord through a community through any means other than violent ones? Am I just not noticing an obvious piece of information?

I would go with only communicating with a languages you know or images. 

I think the fact that certain forms of telepathy specifically state that a shared language isn't necessary implies that, by default, general telepathy doesn't bypass language barriers in and of itself.

On a related note, does telepathy give one the ability to be aware of other minds in the area? Certain ones say creatures you can see, others do not.

For spells and playable races, refer to the spell or racial trait. For feats refer to the feat.

For Monsters that list Telepathy as a language, use the rules as detailed in Monster Manual.

Telepathy

Telepathy is a magical ability that allows a monster to communicate mentally with another creature within a specified range. The contacted creature doesn’t need to share a language with the monster to communicate in this way with it, but it must be able to understand at least one language. A creature without telepathy can receive and respond to telepathic messages but can’t initiate or terminate a telepathic conversation.

A telepathic monster doesn’t need to see a contacted creature and can end the telepathic contact at any time. The contact is broken as soon as the two creatures are no longer within range of each other or if the telepathic monster contacts a different creature within range. A telepathic monster can initiate or terminate a telepathic conversation without using an action, but while the monster is incapacitated, it can’t initiate telepathic contact, and any current contact is terminated.

A creature within the area of an antimagic field or in any other location where magic doesn’t function can’t send or receive telepathic messages.

That doesn't tell us if you can sense those around you if they were invisible.

Quote from Flynn >>

That doesn't tell us if you can sense those around you if they were invisible.

I did reply to you on your thread regarding telepath and invisible people, here.

Telepathy does necessarily let you "see" or be aware of minds. However, since telepathy does not need to know the location of the creature as long as it's within range, you could speak to it, but it does not need to respond, which your character wouldn't know if something was there if it did not. Since telepathy alone does not allow you to "detect" creatures and only initiate conversation, to tell if a invisible creature is in the room, or area, casting detect thoughts would be required to detect a mind.

Does telepathic feat's capability work on polymorph? If I turn myself into a giant eagle, which can't speak but know common. Will I be able to telepathically speak to others without need to move my mouth?

Quote from Bobstery >>

Does telepathic feat's capability work on polymorph? If I turn myself into a giant eagle, which can't speak but know common. Will I be able to telepathically speak to others without need to move my mouth?

Polymorph means you replace your stats with the form's stats: that means you lose your feats. So, the answer is no because you will no longer have the feat and the telepathy it grants until the polymorph ends.

You do retain it if you Wild Shape (Druid feature) or use the Shapechange spell since it lets you use your class abilities (which includes feats, if obtained through the class ASI). 

Good to know, thanks.

Quote from Cyb3rM1nd >>

Quote from Bobstery >>

Does telepathic feat's capability work on polymorph? If I turn myself into a giant eagle, which can't speak but know common. Will I be able to telepathically speak to others without need to move my mouth?

 

Polymorph means you replace your stats with the form's stats: that means you lose your feats. So, the answer is no because you will no longer have the feat and the telepathy it grants until the polymorph ends.

You do retain it if you Wild Shape (Druid feature) or use the Shapechange spell since it lets you use your class abilities (which includes feats, if obtained through the class ASI). 

 What about comprehend language + telepathic feat? Would that work, or it had to be tongue?

There is nothing in the description of telepathy that says you can search for minds, or sense them. You can communicate with beings you know exist within range. No line of sight required, but nothing about that ability suggests that you can detect a mind that you are not aware of.

What about Advanced Telepathy as a racial trait how would that work?

What do you mean by "Advanced Telepathy"?

If you are talking about a homebrew racial trait, then that's entirely up to the designer. My first stab would be something like the following:

Advanced Telepathy

At 1st level, as normal Telepathy
At 5th level, the character can cast Detect Thoughts as an action, once per long rest.

Akin to other scaling racial traits.

So essentially you can yell with your mind up to the range of telepathy, and not know if anyone hears you unless they respond? At which point you can make a link? 

Quote from C3ii >>

So essentially you can yell with your mind up to the range of telepathy, and not know if anyone hears you unless they respond? At which point you can make a link? 

 This is all the rules we have on telepathy as a baseline creature trait.  You can't "shout" because telepathy can only be "heard" by one creature at a time, like an email with only one recipient.  The rules, as you can see by clicking on the link, are entirely silent on how a telepathic creature selects/specifies which target creature should be the recipient of a telepathic message, other than being explicit that it doesn't require sight and does require range.  Your DM can invent any rule they like within those constraints and stay within the RAW, so it's up to your DM if a telepath can e.g. send a message to "the closest recipient" or "a recipient named Bob" or "a recipient which is an ooze" or whatever.

"A telepathic monster doesn’t need to see a contacted creature and can end the telepathic contact at any time" 

When it says contacted, do you believe it implies previously contacted? In that case, what are the criteria for being able to make the initial contact...?

And if the telepathic monster can just contact any creature without seeing them, within a certain range and only one at a time, then wouldn't that imply some sort of inherent way to distinguish creatures between creatures in range?

I would think the creature needs to be known to the telepathic monster, but if that were the case why would they specify not needing to see the contact without establishing another way of knowing the creature's existence. 

Another question on the same topic:

My party is in the Feywild and they have signed a contract which forbids them to insult someone out loud. Could they do it via telepathy and just scream in the Fey's mind? Or can the recipient of the telepathic contact decide to not accept and block the "sender"?