my understanding is that a Casting Tablet forces your Gift to produce magic in the same way as the author of the Casting Tablet.
Thus in order to use a Casting Tablet, you need the Gift, and the ability read what the author wrote. So Latin at high enough level., and Artes Liberalis for reading.
And Hermetic Magic Theory to understand the terms the author uses?
What level though?
Surely Josephus Bloggus, a Gifted yet not magically trained, but with strong reading skill in Latin can't pick up a Casting Tablet and cast it, or could he?
I wouldn't even require understanding of what you are reading to use a casting tablet. So no magic theory and not really hight latin. Casting Tablets are designed to allow gifted people to do things they otherwise cannot do, so asking for them to really know what they are doing kills the point of it for me.
Also I like to hide traps and tricks into casting tablets, if the caster could understand what he is doing then I couldn't do that.
Why wouldn't he? One could argue that one need to have had the Gift Opened to the Hermetic Arts before you can use a casting tablet, but even that would more or less be a house rule.
Casting Tablets are specifically created so magi can cast spells they are not knowledgable enough to learn normally, so they are supposed to be usable by someone with minimal skill and knowledge.
The rules for casting tablets do not mention any requirements for using a casting tablet, but enough skill in Artes Liberales so you can read the text can be assumed, as well as sufficient skill in the language used (typically Latin) so you have clue how to pronounce the words.
A Casting Tablet requires you to generate a TeFo casting total. A Gifted person who hadn't the Gift opened to Hermetic Arts can't generate one. Therefore:
Barring some houserule he couldn't, because he is incapable of generating a relevant casting total.
Assuming the tablet was written in Latin, yes for the first two. It's not specified that it needs to be written in Latin, but since those are direct instructions to cast the spell I'd assume that's indeed the language (except for places like Thebes, where effort was done to change the language of casting, and you might very well have a casting tablet written in Greek).
Any particular degree of Magic Theory, however, should be unnecessary.
I thought it was obvious that the arts had to be opened, but maybe this is reading the rules as a mathematician which I have elsewhere argued that one should not do.
It is when the arts are opened that you get a score of zero. With unopened arts there is no art score. Using a casting tablet requires a casting score, defined as a sum of some arts and some other things. Without art scores there is no casting score, and hence no casting.
Yes, I do like the idea of casting something you could otherwise not do at all, so maybe one should have casting tablets that did not depend on the same casting score as if one knew the spell. OTOH, I think that is a variation of charged items and not one of casting tablets.
And BTW, I would allow casting tablets in any language, but require knowledge of the language used; to me there is magic in words, and not pronouncing the words makes it harder to cast. Bad pronunciation should give bad magic (aka botch).