1

I would like to know if there are any rules regarding the use of either the roman or the arabic numerals.

I am currently writing a relatively important document, and I am not sure which one to choose.

Moreover, is it acceptable to use both?

I. Title
  I.1 subtitle
    I.1.1 ...

II. Another title
3

Roman numbers are hard to read and confusing. Use simple numbers 1,2,3,4.. If you have any sub sections make it as 1.1, 1.2 ...

Using both roman and arabic numerals will be difficult to identify if the list goes on. So I would suggest you to use only arabic numerals.

I recommend you to read this article written by 'Matthew Butterick' in his book practical typography.

There are no rules but only guidelines.

2

The rules about numbering and bullets are specific to the institute/firm/organisation you work/study in.

In general, the use of Roman numbers is not recommended considering the fact that younger generations do not understand them properly.

The current tendency is to abandon their use entirely.

For example:

Rome finally abandons 'too complicated' Roman numerals

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