There are a ton of Scots dialects and they haven't got any standardised orthography either. It's pretty funny. That said, when you hear a Scot speaking, it's not exactly standard English either. I still don't know what to classify Scots as. But it's definitely fun stuff - not tried my hand at it, though. The point is, you speak Scots (whatever brand) but you write English (at least usually; maybe some people write door signs a la Robbie Burns, but that you'll have to tell me more about).
but I don't think most mainstream education classes teach anything particularly well, either!
That is correct. But let's keep it at history, geography, and languages (teaching science is another kettle entirely and I have a lot of gripes with most education systems in general). Suffice it to say that teaching French verb conjugations doesn't make you speak French (and nor does teaching Scottish Gaelic grammar make you automagically speak Gaelic). The single most definitive factor in the ability to speak a language is how often you use it. That sounds stupidly simple but it's true; 99% of people can learn a foreign language (though they might skimp on details/accent) if they use it consistently every day. One thing classes should be doing is immersing children in the language - being in French class should mean you're speaking French (and being in a Gaelic class means forcing the children to speak Gaelic during that time).
This question isn't really about independence, but I don't see why we should have to be complacent with a government that doesn't represent the nation as a whole. We have nuclear weapons that we don't want stuck in our country because the UK government refuses to move them. Our interests are entirely different - we returned one Conservative MP in the 2011 general election. One. 'Exchanging' Cameron for Salmond might not make things ~*~better~*~ but certainly they'll be more representative of Scottish interests. Which the UK parliament really isn't. We're interested in social change, not beating the NHS half to death. (Although we have been laying off a lot of nurses, which is worrying.)
The problem really is, that becoming independent doesn't do you any good. It doesn't really solve a lot of problems; the problems that need solving would be equally well off with a UK government that wasn't hopelessly incompetent. If you become independent, this doesn't absolve you from a lot of stuff: trade relations, diplomacy, educational system reforms, foreign policy, defense, the list goes on and on. In 95% of the cases you are going to still be linked to the rest of the UK because it's the majority of your trade. You're still going to be involved with EU regulations because it's an important part of your trade. Effectively becoming independent will give you a little bit more leeway on some social issues, but things like nuclear weapons will not be solved because you have become independent.
The Netherlands is an independent country, but 90% of our laws and regulations are still forced on us because we are an EU member and have to comply with it because of foreign trade. Scotland, Northern Ireland, all those other countries (Catalonia, the Belgian parts), etc. can want to be independent all they want, they're dependent on the import and export with their neighbours. That economic bond is always going to exist and by becoming independent you may be able to vote more autonomously but the policy will, sparing a few local details, not change an inch. In that sense it's worth debating whether there can't be a better in-house autonomy solution for Scotland, since in the main SNP policy is not going to deviate too much from what is happening now.
I agree with you that there are Scotland-specific issues that need to be solved, I am just highly skeptical that independence will solve them. I admire the Scottish tartan pride, but I think independence will not really change all that much. But if it gives the Scots the impression that this was their choice and they don't have the feeling it was foisted on them by England, then I guess that particular symbolic statement will have to do the job.
By the way, one sad story I recently heard was about a cute Scottish girl I met at a polyglot meeting here in the Netherlands who had lost her Scottish accent. As if the English accent was more prestigious...