Some travel agencies, including online ones, will have AS process the charge for AS tickets sold through their office/website. In that case, you should get the triple miles. In the case of booking on another airline's website or call center, you will not get the bonus miles as Alaska is not selling the ticket (the ticket number would begin with 027 if it was sold by AS) and you would likely be flying on a codeshare operated by AS rather than an AS-marketed flight.

The flights you are seeing on AA are likely AA flights with some segments operated by AS, ie AA 6759 operated by AS as AS 451 LAX-SEA. AA.com can sometimes book AS (and DL/UA) flights without the AA codeshare when using the All Airlines option, but the ticket will still be on AA (001) ticket stock.

AS will let you book partner and even many domestic UA/CO/US flights provided that you have at least one AS-marketed flight in your itinerary. For the most part, you will have to call AS within 24 hours of purchasing the AS flight online to add segments on other carriers. There is no phone booking fee for these changes, but your ticket will no longer be subject to the 24-hr after booking cancellation policy. From my discussions with AS agents, they may be able to book some AA and DL codeshares that are operated by AS as long as you have an AS-marketed flight in your itinerary. It's also possible to combine AS and some DL/AA fares online by using the multi-city (by price) option on alaskaair.com.