There are already lots of ways to immortality in the present rule set.
No, it's the Limit of Aging, a separate lesser Limit, and the Mystae researchers have developed several effective ways of defeating it, showing it is but a flaw of Hermetic magic, like most of the lesser limits.
I've always been most-partial to figuring out ways to copy or steal Inscribed Memories (which is to say, Arts and Abilities).
I think that a magical internet and to a lesser degree the printing press would indeed change the order a lot. It could be a precursor for huge number of breakthroughs - suddenly information could be shared instantly and inexpensively. Could be the beginning of a sort of magical singularity, the same way the information society is considered the beginning of a technological and scientific singularity.
For an organisation in the middle ages to have access to widely spread and cheap instant communication... could very well change everything. The church and the nobles might be more powerful in terms of raw power, but the order would be faster and better at everything. This opens up for actual world domination and illuminati scenarios... though only until God decides that it isn't part of It's plan and dispatches Michael or Abaddon to stop them. Then it would be game over I suppose.
This could all be a consequence of breaking the limit of vis actually. Spells are available for copying books and instant communication, it's just that the items and rituals require a lot of vis. This could also make for a cool political group or mystery actually - someone trying to create enough items for communication and distribute them so everyone can quickly communicate. Sort of like the portal network that was made in Irish tribunal.
This is a possibility contemplated in A&A, right?
Not that I recall. I think I simply made it up.
No. A&A (p.22) discusses the possiblity of using Aristotelian categories to expand Hermetic magic. Ideas include using Quantity to multiply items without need of vis, Time to create a new Technique which changes the position in time of an item, Passion to make "reverse" Hermetic spells (e.g. using Herbam to burn a log), Relation to manipulate Sympathetic Connections, Possession to do away with casting requisites to affect a Form and to manipulate Arcane Connections. The latter two insights could be combined in the same new Technique. However, these possible Breakthroughs are only given as very summary suggestions and not developed in any real way, nowhere as the Brekathroughs exposed in AnM and HM, anyway. A&A (p. 11) also mentions fusing Hermetic Theory with Aristotelianism or Platonis, but these are Minor Breakthroughs of limited value: all the benefit thay would do is to add Artes Liberales score to Lab Totals and formulaic spell casting totals.