1. Will I lose marks for spelling mistakes like 'Appril' instead of 'April'?
Yes, 'Appril' would be marked wrong in the listening and reading tests.
2. Can I suggest reasons for changes shown on graphs or charts?
No, you shouldn't try to explain reasons for the data in writing task 1. Just describe what you can see.
3. When should I use 'the' in the phrase 'figure / figures for'?
You can use 'the' with the singular and plural, but I often miss it with the plural (i.e. "the graph shows the figure for" but "the graph shows figures for").
4. Is it a ok to start task 2 essays with a question?
No, that would be more journalistic than academic style.
5. In writing task 2, is it possible to agree completely but still mention the other side?
Yes, you can mention the other side of the argument too, but make sure it's clear that you disagree with it, and explain why.