Can anyone clarify to what extent, under the law, do illegal immigrants have rights?

I would suggest contacting the police like you would for anybody else. If this causes a legal issue you may offer to assist the immigrant in some way; Perhaps even sponsor them.

I think that depends on what the “poor treatment” is, and they might just get deported.

Here’s the ACLU site about immigrant rights.

Here’s an article about the terminology used. They should be called undocumented immigrants.

The AFSC site on immigrant rights should help. There are plenty of organizations there, perhaps one in your area, that might help. Their page on Immigration Law and Policy might also be useful.

That should give you a good start. There are plenty of organizations that deal with this.

“illegal citizens”? Yes I also prefer “undocumented immigrants.” Not citizens (of the USA) as far a I am concerned.
A human rights violation is a human rights violation. No matter what.
Them being illegally in this country? That is another discussion.

What legal rights do illegals have?—that’s a bit of broad question. I’m pretty sure they have most of the same US Constitutional rights as US citizens (voting rights, and particular jobs coming to mind as 2 of many exceptions), though Congress can discriminate against illegals based on race as part of its immigration policy. As far as I know, states are more or less limited in this area.
“Poor treatment” is also pretty vague, maybe you could more specific. Is the cashier at Safeway giving them a dirty look, or are they being severely beaten with hammers by the local authorities? The first is arguably ok, the latter is a definite no-no.
Any guess at answering your other 2 questions depends on what it is actually going on, which is unclear.

The state of the law in regard to undocumented aliens/illegal aliens is unsettled at this time and the extent to which they have rights is one of the main areas of uncertainty. The Government, through its attorney’s maintains that the rights available to illegals are very limited and circumscribed by ,imho, some very bad law.
To involve the police or other government agency would be to place these people at their mercy. This is the quandary which illegals face all day , every day.