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I don't believe there is any "easy" way to get past her lab. What I can say is that you should go through the classes in the academy again and pay attention to what's said, and then save right before her fight. In order to get past her trials, you end up needing to remember the lessons you attended during the day, such as the multiple choice questions asked in the life magic class, as well as puzzles from previous portions of the game. Nothing changes from attempt to attempt, so you can see what works, take notes, and try again without the frustration of having to figure it all out over and over each time you repeat. Unfortunately, the whole process is timed, so you'll eventually have to do it all fairly quickly.

I believe they're in the forest south of Lakeview (From chapter 2). If that's not them, try the Volcano South East of Lakeview (Again, from chapter 2)

Oh.. uh ... yeah ... sorta know the feeling ;>_>

You get the dictionary from an orphan girl in the slums of the Royal Capital. In order to get it from her, she wants "Any book on Elves" you can find. The book in question is located in a shop, also in the Royal Capital, near the main markets. It's not bought at a counter, but lying around in the store, itself. Look for a shining spot.
1) Look for a book lying around a shop in the main market area of the Royal Capital (Doesn't cost any money)
2) Trade the book you found to an orphan girl in the slums of the Royal Capital for the Elvish Dictionary
3) Go to the Elf in the forest West of the Royal Capital (with the bees). She's located near a statue of the Goddess
*BONUS* Once she's living in your mansion, she'll eventually want you to get her some mushrooms or something for her cravings. Somewhere East of the Royal Capital, there's a place you can land the boat and explore. Inside this little zone is an Elf that says you can't go any further, but looking around the area (another shiny spot) you'll find the mushrooms you want. Return to the Elf in your mansion and present your prize

Sadly, it's not just when you summon it. I did a little experimenting, and excepting the 1st boat ride to get down to the Royal Capital, the boat is completely inoperable. The very next time you see the boat is after you escape from prison and wake up in Neko Village. The boat is then waiting for you just north of town at the dock as soon as you regain control of your character, with no summoning necessary. Even then, it freezes game play.

Edit: It's also possible I got the "Cosmic Ray" treatment for my boats .... I'll do something extreme like delete and redownload the whole thing and start fresh, see if anything changes

When fighting Bastet, you must 1st kill the spirits, as you've figured out. When then prompted to use the "summon spell", you have to go into Sanura's spell list (NOT Goddess abilities), and for this portion of the fight, she gains a new "Summon Spirits" spell.