Currently away from books, and a question arises.
Is opening the Arts of an Apprentice a lab activity? I am 90% certain it is, but I don't know where that is explicitly stated.
How did Pralix teach Hermetic Magic to ex miscs? Or a travelling Maga finding the perfect apprentice candidate?
Yes, it's an InVi lab activity. It's explained in the laboratory section of the core book, p.106-107.
It's possible to have a mobile laboratory, just as it is possible to get arround the travel problems with sufficient magic to speed up return to your lab with a new recruit.
Peregirinatores might find hospitality and a lab in a Rhine covenant, if they show a promising kid and ask nicely. Refusing them outright would be interference with their Oath of Hermes and badly reflect on the covenant.
I think it would be best for a peregrinatore to acquire a guest spot and lab at a Covenant before beginning the search for an apprentice. Not least because they're not legally your apprentice until you have (begun the process to) open the arts, and so anyone can legally take them.
The guest spot is payable, and although the system is rather fair and predictable, it is worth saving the vis and possible obligations if you can.
One possibility is to set up a temporary lab specifically for the purpose of opening your new apprentice's Gift. That takes a season for a basic lab (Quality -3) and doesn't cost much.
Another is to have a mobile lab that you travel with. A very large wagon might be able to do the trick. It would be severely limited.
A third possibility is that the peregrinator has established a more permanent base somewhere in (or even outside) the Tribunal, where he has a lab. It's not a covenant, and is only protected by the fact that it is hidden away in a place no one knows about, and possibly by his sanctum marker. For example, the peregrinator might be the owner of a town house where he installed his lab. Or he has a cave that's been set up as a hiding place with a lab. It is probably not in a place with a high magical aura, since that might draw the interest of other magi. Or it may be very well hidden (such as in a regio).
Note that in the Rhine, the status of a peregrinator is simply the fact that you are not an official member of a covenant. It does not mean that you constantly travel around. You might have a circuit of 2-3 covenants that you visit a few years at a time. Or you may simply live alone in a quiet place, much like an eremite does in the Normandy Tribunal.
... if that anyone knows what they might get by claiming this apprentice. The peregrinator knows, and also should know whether the approached covenant is desperate enough for apprentices to take just about any Gifted kid. 
Keep in mind that it is possible to have a lab without a covenant. All you need is 500 sq ft of enclosed space, a magic theory of 3, two seasons of work, and five MP worth of equipment. If you can locate a Lacunae in a city where there is such a room for rent you are in business.
Additionally while opening an apprentice is a lab activity, teaching magic theory is not. So if you find a foreign magical tradition that is willing to join the order you can teach magic theory to the current practitioners and then establish a lab with them to open the apprentice in.
She cheated, as did all the founders and big names characters.
Lets pretend she has the following virtue.
Assimilation - When opening the arts to a gifted person, she does not need a lab and when making the stress die roll test, all odd numbers act as a 1.
Alternatively, we could go with the simplest explanation: she set up a lab somewhere, and took her apprentices back to it.
The amount of people Pralix taught just doesn't work within the current game rules. It is a season to open a person arts. Also, does she stop then? They'd be absolute patsies with 0s in every technique and form. The force she got together was enough to take on Damhan-Allaidh.
Nothing in the rules would allow a character to start with Creo Ignem of 15 each once their arts are openend, but arguably, that's what happened when Flambeau became a hermetic mage.
Trying to put the narrative elements of the founders in to current rules (without inventing unbalanced virtues) is near impossible.
Depends on how many years she had to do it. Teaching can spread quickly when you draft in your students to teach the following generation of students.
You don't have to provide deep training in all areas. Teach subject 1 to the first student, subject 2 to the second student, and so on, and then the students can teach each others.
Once you've covered a decent variety of subjects, and your students have begun teaching the second genetation, then you deepen the knowledge of the first generation.
The students can also start studying from raw vis once their Arts are open None of this requires a lab. The student don't even need to learn Latin and Artes Liberales, which they would need to study from books.
But from what I can remember, the main thing she taught was Parma, so that her army would have a better form of magical defense against D-A.
I think that's the key. She might not have opened their arts, but instead relied on their non-Hermetic powers and the Parma for victory. Hermeticising the various sub-traditions came later.