Composition multiple choice questions, also called "writing multiple choice questions," are intended to measure your writing skills by asking you to act as an editor and improve the organization, clarity, and grammar of several passages written especially for the test. In other words, these questions require you to read a passage, identify mistakes and weaknesses, and fix them. These questions are essentially slightly-harder versions of the questions on the "Writing and Language" section of the SAT or the "English" section of the ACT.
The test will include 20-22 composition multiple choice questions. That's a little less than half of the total 45 multiple choice questions that make up the test. The 20-22 questions will be split between three different passages.
Becoming a better writer doesn't happen overnight, so unfortunately there's nothing you can do to "cram" for these questions. There's not a specific set of rules or skills that you can memorize. Becoming a good writer takes time, patience, and practice. Studying grammar rules can be helpful, though you don't need to go overboard; composition questions tend to measure your ability to effectively communicate and organize ideas far more than your ability to write grammatically correct sentences.
Thus, the best way to prepare for these questions is to...
1) Start paying close attention to the ways professional writers construct their texts. Thinking carefully about how writers present their ideas, how they transition between paragraphs, etc. will increase your understanding of what effective writing looks like.
2) Think deeply about the choices you're making when you write essays of your own. Instead of throwing something on the page forty-five minutes before the essay is due, spend a significant amount of time revising your essay. Rewrite entire paragraphs. Find new ways to transition between ideas. Try out a few different attention-getters and see which one works best. Think carefully about how individual words affect the tone & meaning of your writing. Revise, revise, revise. Essays are never perfect. Consistently being hypercritical of your own writing will make you much better at composition questions, which ask you to be critical of others' writing.
3) Complete practice questions. In addition to the practice questions I give you in class, you may want to complete practice questions on your own. Composition questions were added to the AP Test very recently, so if you Google "AP Lang writing/composition multiple choice" you'll get a few, but not a bunch of, results. Nonetheless, if you exhaust all of the resources you find in your original Google search, you can always practice SAT writing questions and/or ACT English questions. Those questions aren't identical to AP Composition questions, but they're close enough that they will still provide you with some helpful practice.