My friend and I?

Actually, the pronoun should be in the subjective case (I) because it is one of the subjects of the verb sitting.

Thanks. Just sounds so wrong in the next photograph where my friend has gone and it's just me: "I sitting by the river".

xdzgorJust sounds so wrong in the next photograph where my friend has gone and it's just me: "I sitting by the river".

Yes, it does sound wrong as the only subject. Most of us would informally say This is me sitting by the river, whereas formally, it would be better to say This is a picture of me sitting by the river, since This is I sitting b

xdzgorMy friend and I sitting by the river

If it's an abbreviated form of "This is my friend and ___ sitting by the river", which I take it to be, then you need the post-verbal form "me" because it's after the (implied) verb "is".

CJ

Not according to Aspara Gus. The correct form would be "This is I sitting by the river".

xdzgorNot according to Aspara Gus.

Yes. I noticed that. Opinions vary regarding the correct case of a pronoun after a linking verb form like "is".

This is I is perhaps an older form.
This is me is currently more used.
That's why I advised the latter.

CJ

CalifJimThis is I is perhaps an older form. This is me is currently more used.

I'd like to clear up that I accept both forms. The former is just more formal.

Aspara GusI'd like to clear up that I accept both forms. The former is just more formal.

That's how I understood it as well. I'm not sure the OP understood it that way.

No - I am not sure how to understand it. I gather now, that both forms are "correct", one is just "formal"?
Personally, I could also say "me and him went to the river" - is that correct, but not formal, or is it simply not correct?

xdzgorme and him went to the river

Simply not correct.

It's before the verb ('went') so it should be "He and I".

CJ