tough_choices

Yeah, most of the first year curriculum is filled with core classes, with electives and the capstone during the second year. For the MIA a typical first year is:
Fall
GPCO 401. Microeconomics for Policy and Management GPCO 412. Globalization, the World System, and the Pacific  GPCO 453. Quantitative Methods I  Language Winter
GPCO 400. Policy-Making Processes GPCO 415. Accounting and Finance for Policy Makers  GPCO 454. Quantitative Methods II  Language Spring
GPCO 403. International Economics GPCO 410. International Politics and Security Language Elective Of course, if you're in the MIA but don't have to take language classes this opens up a lot of slots for electives. Some people also waive core classes, but this is pretty hard to do. (For example, I was an econ major in undergrad but was only able to waive QM 1.) Last year a lot of people wanted to waive International Security but weren't allowed to.
The career tracks usually only require two required classes and three electives (from a broad list), so there's a lot of room to customize them. While there is no waitlist for any GPS course unfortunately classes are only offered once a year and sometimes not every year (this is pretty rare). In a two year program this means that scheduling conflicts may mean you miss classes you want, and I wouldn't recommend choosing to attend GPS based on one specific course you want to take since you might not be able to.
I only took one Spanish class at GPS so can only speak to that. I *believe* that Spanish and Chinese are only offered at GPS from the intermediate level up, so if you are just starting you would have to take undergraduate classes. Otherwise you would take the intermediate+ courses at GPS. I've heard complaints about the undergrad classes from people in my cohort (the undergrad language classes are five units and like 6 hours per week, more than GPS language classes), and personally had bad experiences in UCSD Spanish classes years ago as an undergrad. Your experience in other languages may be different, however. If you really care about the language course offerings I would encourage you to ask admissions.
One thing to potentially be aware of in the MIA is that international students can only waive the language requirement if they are native speakers of a GPS "Pacific" language—good news if you're from east Asia, not great if you are from Africa.
I don't know. 
The hands-down best instructor at GPS is Craig McIntosh, who teaches QM3 and QM4 and some of the development courses. Jennifer Burney who teaches QM2 is also good, as is 
Stephan Haggard who does Globalization and Asian security stuff. In environmental and energy policy David G. Victor is very famous and is a good lecturer. I haven't had either of them but I've heard good things about the new economics and marketing professors Uma Karmarkar and Renee Bowen. Bill Bold, who was a former VP at Qualcomm, just started teaching business classes and is a great lecturer and assigns lots of assignments with real-world feels.
I've taken mostly energy and business/finance, so only know those professors personally. Aside from these standouts most GPS professors are good-to-average. Unfortunately some professors are boring or bad lecturers, and there are two or three older professors who are disorganized and poor to very poor teachers. Aside from them I have been pretty satisfied with the overall quality of the teaching, though some students disagree.

I was also offered full funding, and my official letter correctly stated one year of non resident tuition and fees and one year of resident tuition and fees. Maybe worth emailing the GPS admission office about it? Sounds like they must have made a mistake in your letter.