Yes, this feature is called clusivity, there are dozens of languages that have it, for example Mandarin Chinese, Vietnamese, Malay, Hawaiian, etc. This article has a list of such languages together with their inclusive and exclusive forms of "we": Clusivity (Wikipedia).
This distinction is called clusivity and as far as I know no language has a three-way distinction here, having at most a two way inclusive (1 & 3 in your list), exclusive (2 in your list) distinction
The relevant chapters on WALS (a very useful resource for checking things like this) can be found from the corresponding maps here (for independent pronouns)...
There are some languages where the inclusive forms clearly pattern separately from the second person forms. One such language I've studied is Walmajarri, an Australia language. Here are the subject agreement markers:
This is called clusivity, and although not found in European languages (AFAIK), it is found in South Asia and Australasia at least.
An example of how this is used (as taken from Fantastic Features We Don't Have In The English Language (YouTube)):
We've just won the lottery!
In English this is unclear - is the listener included? If English had an ...
I haven't got enough reputation to comment, but I must add this link because WALS is such an amazing tool for these type of questions:
Inclusive/Exclusive Distinction in Independent Pronouns
This will show the answer to your question on a map. Explore other features by clicking Features in the menu.
In American Sign Language, pronouns are indicated spatially, so it is very easy to make a clear distinction between the three cases:
2- or K-handshape back and forth for "you and I" or "two of us"
1-handshape from side to side of chest, pointing to the speaker, for "we" meaning "they and I, but not you"
1-handshape in ...
The Malayalam language (of which I am a native speaker) makes a distinction, as does Sanskrit.
E.g., in Malayalam, "nammal" (us, you included), "nammal iruvarum" (the two of us), "njangal" (us, you excluded). The second of these is a bit of a long shot; since it literally means "us two".
There are languages that have a dual/plural number distinction as well as an inclusive/exclusive distinction in the first person, so there definitely could be separate inclusive first-person pronouns corresponding to "[me] and [you (sing)]" and "[me] and [you (plural)]". "Inclusive/Exclusive Distinction in Independent Pronouns", by Michael Cysouw (Chapter ...
There are interesting pragmatic consequences to using 1st person inclusive (1INC) in certain languages, e.g. in Tamil, 1INC is used by lower-caste members as a 1st person form to address higher-caste members. This may be taken to suggest that 1INC is fundamentally a 1st person form, but in Santali, 1INC is used as a 2nd person form in order to threaten ...
Norwegian Sign Language distinguishes between inclusive and exclusive "we". Apart from that it distinguishes between dual and plural, so there are different signs for:
we (2 people, listener excluded)
we (2 people, listener included)
we (more than 2 people, listener excluded)
we (more than 2 people, listener included)
I don't know about other sign ...
In Vietnamese there are 2 types of "we":
inclusive we: "chúng ta", to address the speaker, the person spoken to, and maybe others if any
exclusive we: "chúng tôi", to address the speaker and others, excluding the person spoken to.
This was asked here: Is there a language which distinguishes between three types of "we"? (1) speaker and person spoken to (2) ...
Malay (Malaysian/Singaporean, Brunei & Indonesian) differentiates two "we":
Kami - them and I but not you
Kita - all of us
The case of just you and I can be covered by "kita berdua" which is literally "we two" or "the two of us" but that is kind of a cheat and is not literally a word.
Tamil also has this feature.
Nāṅkaḷ kāṭṭil-ukku pōkiṟōm
We, (not including the person being adressed) are going to the forest.
Namma kāṭṭil-ukku pōkiṟōm
We, (including the person being adressed) are going to the forest.
I think it's just convention. If a pronoun includes in its reference the speaker then we call it a first person pronoun. If a pronoun includes in its reference the listener, then we call it a second person pronoun. If neither the speaker or listener are included then we call it third person pronoun.
Spanish language has distinction by gender(wiki) for the pronoun "we"(nosotros/nosotras):
... also inflect for gender: nosotros and vosotros are used
to refer to groups of men (as well as men and women), and
nosotras and vosotras are used exclusively to refer to groups of women.
Tongan allows for this (and I suspect other Polynesian languages as well). Each pronoun has a singular, duo, and trio+ form, and each of the first-person plural pronouns have both inclusive and exclusive forms (for including or excluding the listener).
Mandarin Chinese has "我们" ("wǒmen" can be inclusive but not necessarily) and "咱们" (" zánmen" almost always inclusive), though there are additional register and regional differences ("zánmen" is mainly used in conversation and in the north). More info on Chinese Stackexchange.
Hawaiian allows for all three of these uses to be distinguished. This is because it has not only clusivity but also a dual number (so that plural implies at least three). 1 would be inclusive dual, 2 exclusive plural, and 3 inclusive plural. (Exclusive dual would be “me and one other person who isn’t you”.)
Linguistic description of Berber languages does not mention the clusivity as phenomenon that exists in Berber. However, according to me, such particularity is present in Riffian at least for the inclusive. This form is generally considered a imperative form, but it is not the case.
Inclusive "we" is only used in the future tense and is constructed like this:...