1) In the reading test, are the answers for "summary completion" questions in order in the passage?
Usually, yes. I've seen one or two summary questions where one of the answers breaks this rule, but you can assume that answers will almost always be in order in the passage.
2) Is it ok to write "T, F, NG" instead of "True, False, Not given"?
Yes, I've been told that "T, F, NG" is fine (although I prefer to write the full words).
3) My teacher told me to avoid using "Firstly, Secondly, Finally" because too many other students will use the same words. What do you think?
I disagree. Examiners are not comparing you with other students, and they care much more about the content between the linking words than the linking words themselves. Read this lesson.
4) Is there a maximum number of words in the writing test?
No, there is no maximum.
5) What linkers can I use to improve my "lexical resource" score?
Linkers don't help your lexical resource (vocabulary) score! They only help you to organise your essay. If you want to improve your vocabulary score, you need to use good words and phrases that relate to the question topic (e.g. 'global warming' is vocabulary for the environment topic).