As best I can determine, the return of Myrkul post Sundering is not actually detailed anywhere yet.
There are references to Myrkul in one sundering novel, but they aren't actually helpful to what you're looking for.
In the Sundering novel "The Sentinel" by Troy Denning, there is a character who CLAIMS to be the Chosen of Myrkul through most of the book, but near the end is revealed to be the Chosen of Cyric, the masquerade part of an elaborate plan to let Cyric usurp Myrkul's old portfolio.
In a magical medieval world like FR, I am not sure if it would be easy to find an institution of higher learning that is not connected to theology, military or magic. Even Earth's fair share of universities were founded with religious studies playing a core role.
As a concrete example, consider the so-called City of Splendors, Waterdeep, one of the largest cities in the continent of Faerun, and possibly the most influential. An entire 2e boxed set, and a 3.5e sourcebook was dedicated just to this city. The 3.5e sourcebook describes it to have over 130k population which increases 5-fold in the summer months. The city boasts 12 churches, 4 or 5 arcane schools, a large number of guilds, places to obtain poisons, potions, magical and mundane weapons, a great library associated with the church of Oghma, 11 independent sages (mostly mid-to-high level experts) specialising in various mundane and arcane topics, but only a single organization that is categorised as scholastic, the bardic college New Olamn. No universities at all.
If you decide to expand your question to allow temples and libraries in FR, then the list is a lot longer of course. The most famous of the libraries is Candlekeep. Another one would be the High Temple of Mystra on Mount Talath in Halruaa. Others can be found on the FR wikia. Furthermore, if you allow universities of magic, 3e FR Campaign Setting (FRCS) mentions that it is not uncommon to meet wizards who are university graduates in the lands of Lantan and Halruaa.
Finally, if you want to stick to universities and find the Zakharan and Oriental institutions listed in guildbounty's answer too far, you can try the Great University in Gheldaneth. To the extent that I know, that is the only university that is mentioned by name throughout the whole FRCS. (With its 320-pages full of two-column small-font text, FRCS is arguably the most information-dense sourcebook published on the Realms.) The Great University was one of the two most prominent buildings (the other is the Wizard College) of that metropolis, which happened to be the second largest city in Mulhorand, and ruled by clerics of Thoth. Unfortunately the city survived but got devastated by the Spellplague, so it is not clear what the current whereabouts of the university are.
Best Answer
Yes. There are time portals controlled by Mystra, and one heck of rare 9th level spell to take you there.
Edition notice: Most of the stuff below is from AD&D 2nd sourcebooks. The question does not ask for a specific edition (fluff only) so the content below should be adapted for other editions. Not hard, as the effects do not change game statistics.
The deity of Time in Forgotten Realms (Faerunian pantheon) is Mystra. It is a rather unknown piece of her portfolio, because she really dislikes time travel. This is discussed more in depth in the Chronomancer supplement for AD&D 2nd. Chronomancers are shunned in the Realms, and quickly invited to leave for other Prime Material crystal spheres.
Nevertheless, time travel do exist, in a controlled fashion.
In the Arcane Age supplements for AD&D 2nd, there are mentions of time portals and the time conduit spell, that can take adventurers back in time. One of the plot hooks for Netheril and Cormanthor sourcebooks is to take an adventuring party for a hike back in time.
The same book describes the Time Conduit spell (the time portals work just like the spell):
It should be an epic quest to obtain a copy of this spell. This quest should be done with the blessings of both Mystra and Azuth, and the spell should be used with great caution, else the mage draws the wrath of the deities that control magic itself.
The important points in both forms of time travel are:
The trips are always for a 1-year period. Characters arrive on the early minutes of the first day of the year (1 Hammer) and the conduit brings them back in the night of the last day of the same year (30 Nightall).
All prepared spells, spell slots and psionic power points are stripped from the characters. They need to rest to prepare again their spells / recover their powers.
All spells that do not exist at the epoch of arrival are removed from scrolls and spellbooks. Those are otherwise unaffected. For sorcerers (or spontaneous casters) it would be wise to do the same, temporarily stripping the knowledge of the forbidden spells.
All equipment and items that are not yet invented are removed as well.
Upon return, those equipment and spells (that were removed when going) are returned to their original places. The spellbook will be as it was before entering the conduit/portal.
Most items and spells learned while in the past may be removed by the conduit. Those are forever lost in the timestream.
A whole month (30 days) will have passed (in their normal time-frame) when the characters return.
One cannot go back in time to a epoch where one already existed. You cannot visit yourself. You cannot return twice to the same year.
Time paradoxes are resolved with great prejudice to the one that caused it. This is not an issue when visiting ancient times, as history can rewrite itself over the centuries. But some idiot that decides to become his own grandpa will be erased from the timestream.
If the characters traveled using a time gate, the gate will either move to another location, or the knowledge of the gate location will be removed. One must quest again to find this gate (or one of the others). The spell Time Conduit is not lost or forgotten, but using it repeatedly is a surefire way to earn a visit from Mystra's servants.
I recommend reading Cormanthyr and Chronomancer supplements.
As for psionics, there is the Time Travel psychoportive science. It is described in The Will and The Way Dark Sun supplement (but is available for psionicists everywhere).