Will you be marked down for poor handwriting/sentence structure in exams?

You may be marked down for sentence structure, yes. It’s important to write cohesively so your work can be understood and you can get the maximum points for your ideas! If you are concerned about your handwriting, it may be worth speaking to your teachers about this, as they may be able to help more.

Yes. The examiners often have to mark hundreds of students work, if they can't read it and it is illegible, you will get marked down.

A variety of types of sentences are part of what the examiner is grading you on. As is your grammar, so watch that the tenses match and you don't switch from 1st to 3rd person in the written document.

Handwriting needs to be clear and legible for examiners to clearly understand your writing. Sentence structure is even more important for clarity of understanding and cohesion of your argument. So allow time to review your writing to ensure this at the end. However, depending on the subject will depend on the significance. For instance, it is most important in English Language, and may be less so in other subjects if you have strong subject knowledge, have answered the question clearly and have a well set out argument.

Unfortunately the answer is absolutely yes to this! It’s as important to work on your handwriting as it is your spelling and grammar.