What does this mean? I believe she's just trying to complicate the situation to avoid paying me more money. If I take the landlord to small claims court, must I also take the "authorized representative" in the claim to? Or would I only be filing the claim against the "authorized representative"?
You are still going to sue the individual (landlord), but that person may be represented in court by their representative (attorney).
Currently I only have the email address of the authorized representative. If I need to serve her with documents must she give me her mail address?
I'm not 100% sure about Canada, but usually to serve somebody with a summons or court claim, it must be done in person with a process server or similar service. If that person has an attorney, the papers can be served to either the attorney or the individual in question. Unfortunately you need a physical address of either one to do that.
FWIW I didn't think someone can get out of responsibility like this, when they break the law they say 'you can deal with this person who's acting on my behalf'
That is exactly what a lawyer (attorney) is. They aren't getting out of responsibility, but they are enlisting the assistance of somebody who is familiar with law to assist in the resolution of whatever issue is at hand. Depending on what law is broken, this could be anything from "power of attorney" to a lawyer.
Take for example somebody who sues an elderly homeowner for a minor injury sustained on the property (like slipping on ice). The homeowner could assign power of attorney to, for example, an adult child to represent them in court. The homeowner is still liable, but the child is given the power to represent that person and their interests in small claims court. If the court was a jury trial, the homeowner may need a bar certified lawyer instead. Either way any judgement entered against that person would still be the responsibility of that person (homeowner in this case). You can't assign responsibility to another party.
Other legal terms that pretty much mean the same thing are "duly authorized representative", "deputy", "attorney", "substitute", or "agent". There has to be some kind of formal agreement to be a legal representative, either given by the person being represented or in the case that person is unable to sign, by a court.