dia daoibh gach duine.

Is "deartháir s'agamsa" the same as saying "mo deartháir"?

Does it work the same in normal sentences? Eg: "Bhí deartháir s'agamsa ag léamh..." ?

GRMA

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Please wait for corrections/ more input from other forum members before acting on advice

Yes, in Ulster Irish.

Bhí an deartháir s'agamsa ag léamh... means "My (one) brother was reading" (bhí mo dheartháir ag léamh...)
Bhí deartháir s'agamsa ag léamh... means "A brother of mine was reading" (bhí deartháir de mo chuid/liom ag léamh...)
.i. the article necessary in your case.

No, I don't think so.

s' = seo. The demonstrative adjective requires the article, i.e. an deartháir seo,
deartháir seo without the article (or another marker of definiteness) is impossibe.
But s'agamsa is colloquially often used without the article. But it still means definiteness, lit. "this brother that I have" or simply "my brother".
"s'agamsa" became equivalent to "my".

It cannot be (and isn't afaik) used like "deartháir liom/dom/de mo chuid" which are true indefinite phrases.

While I can't speak for the other dialects, what Labhrás says is certainly correct for Ulster Irish.