some are not true

not ncessarily true: "You will need to file a I-751 one year and nine months after you got married and before your second anniversary. "

You can start to file I-751 1 yr and nine months after you got your conditional green card (if you haven't marry for 2 yr+ at the time you apply for the GC)--not necessarily after your got married. If you married for over 2 years (or 3?), then they probably will give you a permanent GC instead of the conditional one.

You may apply for citizenship 2 yr and 9 months after you got your GC (including conditional GC) if you still marry to the same person. I heard some people got their I-751 process review sooner (i.e. if the condition of the GC is not removed yet) if they apply for N400.

You will probably need to become citizen first before you can apply your mother.