"I and someone", "me and someone" or "I and someone we"

"I and someone are interested" is grammatically correct. It is the convention in English that when you list several people including yourself, you put yourself last, so you really should say "Someone and I are interested." "Someone and I" is the subject of the sentence, so you should use the subjective case "I" rather than the objective "me". "Someone and I" clearly means two people, so you should use "are" and not "is". If it was "Someone or I ..." then you would use "is", because only one person is interested, either "someone" or "I".

It is not uncommon to hear people say "Me and someone are ...", but this is wrong because it's the wrong case. When an educated person hears "Me and Billy is going to the ball game", he immediately thinks this is either a child or a very uneducated person speaking.

"I and someone we ..." is incorrect because it is redundant. "We" is simply another way of saying "I and someone". It adds no new information to the sentence, and so there is no reason to include it. You can't just string together alternative ways of expressing the same idea: If you really need it for clarity or emphasis, you have to surround it with some additional words, like a "that is", or sometimes just punctuation that show its purpose in the sentence. You could say, "We, that is, Bob and I, are interested ..."

All that said, "I and someone" or "Someone and I" sounds strange to me, and I suspect most English speakers, because it is an unusual use of the word "someone". When "someone" is used in a list with identifiers of other people, we usually say "someone else". Like, "Bob and someone else are interested ..." rather than "Bob and someone are interested ..." (I have no idea why this is so; it's just the convention.) "Someone" without "else" is normally only used when it's the only person: "Someone is interesteed ..."

Let me add one possibility no one has mentioned: an appositive.

• Bill and Mark, they’re good chaps.
• Me, I’m thinking of staying.
• Me myself, I’m thinking of staying.
• Your father and me, we’re thinking of staying.
• My partners and me, we’re interested in investing in your product.

All those are grammatical.

The first part of the appositive is not even in the nominative case for pronouns. It might not even be reflexive even if it includes the speaker.

You see this sort of construct in French, too, where the pronoun case for the appositive works the same as in English, deviating from the nominative:

• Moi, je pense que ...
• Moi même, je pense que ...
• Ton père et moi, nous allons ...

In Spanish, however, the nominative is used for the appositive, unlike in English or French:

• Yo, yo pienso que ...
• Yo mismo, yo pienso que ...
• Tu padre y yo, nosotros vamos ...

Can’t tell you why.

I was always taught that you should always put yourself last, which means the correct grammar here is none of your options, but instead it should be:

Someone and I are interested in investing in your product.

The options including "we" are not correct - that structure just doesn't make sense here.

Describe the other person: 'A colleague / a friend / a business associate and I are interested in investing in your product.'