The answers to both of your questions pretty much amount to some variation of "sometimes" or "it depends". I'll try to get a bit more useful than that.

1. Searching for AC published fares booking into P (or Z or D) is pretty straightforward. In the advanced routings area in the extension codes box, type: F AC..&BC=P That will look for all AC published fares with a primary booking class of P.

There are a couple of notable problems with that approach. First, what you're trying to do needs to be fundamentally possible with the fares you're trying to book. I took a quick look at the AC published fares for YYC-JNB and all of the P, Z and D fares that I saw restrict stopovers to one per direction. You may be getting forced into C fares because of that. Some fares will cause stopover add-ons to be applied and some may not permit stopovers at all or may only permit a narrow collection of routings.

Your second problem with the method above is that it will only search AC published fares. While that would be the easiest thing to ticket with AC, it does limit you to a subset of what is actually possible to ticket with AC.

Matrix can be helpful to explore what kinds of fares exist and finding low fare options but Google Flights is usually better for that. What Matrix is really useful for is constructing something you know should be possible after you have already looked at the available fares and decided what you want. Given the nature of the trip you're trying to take, published fares from AC, LH, LX and UA (and any other A++ JV partner) are probably what you want to look at before constructing.

From an efficiency perspective, you probably want to ticket an openjaw going YYC-JNB-YWG with an LHR stopover on the outbound and a FRA stopover on the inbound and get your last YWG-YYC leg on a seperate ticket.

2. AC agents can often ticket something complicated from matrix (provided you find an agent competent enough to custom build and price a route) but not always. The ticketing engine ruleset applied to call center bookings is actually more restrictive than what applies to web booking or TA bookings. For example, the call center will often need the first trans oceanic leg to be either AC operated or AC marketed in order to ticket. That means, for example, if you are using an LH fare basis for the outbound and LH (or even better, UA) metal, the call center ticketing process will fail at issue. TAs can often get around this by selecting an alternate ticketing carrier and so long as there is sufficient AC content on the trip, AC will consent to issue. The web engine ticketing rules are actually pretty loose so if you can build a deep link (using ITA Matrix Powertools or manually) to populate and validate into the website, that will usually work.

I'm not sure exactly what dates you're looking for or how flexible they area but I would use this as a starting point in matrix for construction Matrix URL

In the link above, I've intentionally not specified booking class but have limited it to business class or higher. You can play around and do it either way but this should prompt it to pull seats it thinks are available. The reason I say it thinks they are available is that matrix is really bad at O/D availability. You'll also note I provided some routing guidance - without that, matrix can sometimes fail to return anything but you need to be careful not to be too restrictive otherwise it can limit options or cause search failures.There can be a lot of trial and error involved in building matrix itineraries but it's one of the few ways of getting exactly what you want outside of a really competent TA.