On the matter of the scholar: Summon a swarm of insects. Walk through them, invite the scholar to do the same, even collect a few on their hand and study them and their magical faculties. "Even our pests bow to our civilisation."
Proposals for next round)I am not yet voting for any of these):
Spell of magic crystallisation: Create a tiny crystal out of magic or grow such a crystal to make it larger. These crystals can then be broken down to feed other magic. Essentially allowing our wizards to store up magic during downtime to extend their activities the rest of the time.
Should be a pretty big deal at first, granting us extra power for what we are doing, but might have a downside in that it would mean our casters would often have a combat-useless(Unless it can absorb hostile magic too) spell prepared and be in a magically drained state until they crack open their crystal. So could cost us in enemy ambushes but the extra magic in battles should be a huge boon.
As for future prospects, they are crazy-huge. We could make wands to let civilians and off-duty wizards contribute magic to the front-lines. Probably something like a slot machine, you put your hands on it and watch the pretty lights dance across the magical channels as a crystal slowly grows in a bowl(To keep complexity down they might need to have a seed crystal first, ideally any idiot would be able to use the things.) then they take their crystal to the counter and get paid for their contribution...
Then we develop "wands" that use these crystals instead of needing a proper wizard. We can outfit out mundane soldiers with spells in that case. Arrow summoning bows, self-repairing armour, holy hand-grenades patriotic flame-throwers, spontaneous tower-shields... Making wands for the magically inept would be difficult, it would need to do the whole spell by itself, which would limit it to simple spells, but developing ammunition for such things would be the first step, other than that it is just stripping the spell-process down to its simplest elements and reproducing it in wand-form which is tedious but should be certain.
Another option is to find ways to use extra magic to enhance spells. If we could burn a crystal to make our fog ignore their lesser spells, or turn a fireball into a firesea, or summon the same number of wasps but instead of a few burns a few of them together can melt through metal...
Copy the wind spell: Counter it directly, aid our ships, and gain an element. Having seen it in action should help us develop a copy?
Military academy: Train our thanes and their bodyguards to have consistent expectations and communication. Provide teaching from experienced veterans. Test the lot of them for magical aptitude, and, perhaps most importantly, teach them how to train their followers. Make sure that the whole army meets minimum standards of marching speed, battlefield endurance, responses to cavalry charges and arrow bombardment, knowledge of why running from cavalry is an extremely bad idea... Also they should check their followers for magical aptitude and send them for further evaluation. We can then revise this academy to have a magical faculty to improve training of magicians and to add a magical element to the curriculum so that all squads know a little about magic and can perform extremely basic spells.
At present I expect that we are just relying upon everyone to train themselves. They have good intentions, bless them, but a certain degree of heartless methodical analysis and conformity can work mundane miracles...