Here are my notes from the K lecture. I'll add detail and examples when I have more time.
Critiques are called kritiks from the German because it looks cool and lets us call them K's, which doesn't get confused with other things.
Kritiks do not have uniqueness. This means that it is very hard to blame the Gov for the entire impact of the kritik. The main ways around this are to use the alternative strategically, to turn case solvency, and to try to place the implications of the kritik on a level separate from the impacts of the case.
There are language kritiks and framework kritiks. Language kritiks say that the language you use in round is a reason to vote you down. Framework kritiks say that the assumptions your plan is framed in are a reason to vote you down.
Common language K's are: gendered language (mankind), racist language (ethnic slurs), violent language (we're killing them on the topicality debate), vulgar language (swearing).
Common framework critiques are: capitalism, statism, non-violence (you condone violence), nuclearism (complacency in nuclear weapons), imperialism, colonialism, feminism (here it's usually more that your plan does something sexist or works through the patriarchy), enthnopacentrism (you're-ethnic-centric), anthropocentrism (human-centric, mostly on environmental stuff), _________ism.
A kritik has three parts:
Link, where it is explained what you said or what assumptions you made that the kritik critiques.
impacts or implications, where it's explained why those words or assumptions are bad.
alternative, where it's explained how to avoid the impacts, ideally in a way that means voting against the plan. An alternative is an opposition advocacy other than the status quo (like a counter-plan). It works well to run a counter plan and a kritik- the counterplan functions as the kritik's alternative, and the kritik functions as a net-benefit to the counterplan (as long as the CP doesn't link to the K). Other ways to make an alternative are to re-phrase the plan to not link to the kritik (for example, by fixing the gendered language), or by posing your alternative as just "reject the plan" (this means you have to win the impact comparison straight-up). If you research a particular kritik, you may find good alternatives in the kritik's literature base.
The government can also run kritiks. They can run framework kritiks as a response to a counter-plan, and can run language kritiks if the opposition says something really offensive. This is one time where a new argument is potentially justified in the last speech- if something really offensive is said during the opposition block. Remember, however, if the comment is offensive to you personally, you can make a "point of personal privilege" during his/her speech instead.