It isn't much more confusing than flying with various airlines once the basics are understood. If you want to fly Delta you can get your tickets from a travel agent, or from Delta (in person or online), or from various online services, right? If you want to take an EastCoast train you can get your tickets from a travel agent, or from EastCoast (either online or in person), or various online services. You also have the opportunity to buy tickets on any UK railway company from any of the 26 various railway companies who all can sell each other's tickets.
Just like on airlines, you will get different prices and amenities depending on what day you buy the tickets and from whom. Best advice - run the numbers up and compare.
Does a Senior Railcard give a discount off the Advance fares too?
Yes, in most cases. Read the clearly published restrictions on the ticket sites or at the window.
can we book those fares online in February even though she won't have the senior card in hand?
Yes. But you must have it before you go through the first ticket barrier or on train check with a ticket which relies on the Senior Railcard, and it must be presented with the ticket. In the absence of the relevant railcard the ticket is in-valid, worthless, the passenger must buy a new full-fare ticket and on most companies is liable for a substantial fine.
Not all stations are manned, not all manned ones sell travelcards at all times of the day. It is the passenger's responsibility to have the railcard before travel, regardless. Most larger stations will be able to provide it, especially if you aren't trying to get one at the peak of the rush hour when you will likely be told "immediate travel tickets only at the moment, please".