Difference – ‘Firstly … Secondly …’ or ‘First … Second … ‘?

This purely my subjective point of view. Other people will have other preferences. There is no "right" answer to your question.

If you're writing for an English exam such as Cambridge FCE or CAE levels, please stop after third or thirdly. I've read fourth and fourthly in papers (and elsewhere), and that for me is teetering dangerously on "boring" and "mechanical".

To list a series of points or observations in an essay, a paper, or a formal letter you can start with either First or Firstly; then second or secondly and then use a different discourse marker such as :

• (to contrast) on the other hand; nevertheless; however;
• (to compare) similarly; likewise; in comparison
• (to add) furthermore; in addition; moreover.
• (to conclude) finally or lastly.

1. The two are nearly synonymous, but in technical / numerical contexts multiple is definitely preferred, whereas several is usually used for descriptive contexts like "the user had included several labels", and implies a smallish number (between 3 and ~20). So in your example, multiple is correct. Definitely a stylistic choice though, linguistically and grammatically they are both correct.

2. "Multiple Label and Variables" is incorrect - it should be "Multiple labels and variables". "Multiple Label and Variable Pairs" is also correct but now you are referring to the pairs not the collection of individual things. In your context you definitely mean "Multiple Label and Variable Pairs", but often authors might simply write "Multiple Labels and Variables", or even "Multiple variables", as a shorthand.

3. You probably want: "The user can even specify", the "can even" here implies the of all the things the user can do, this is the one you wish to emphasise. If you wrote "The user even can specify" then the "user even" implies that of all the actors that can specify, you wish to emphasise the user - probably not what you meant! (Worth noting that normal technical prose would shy away from using "even" at all here, I'd say - "The user can specify" is sufficient - depending on context).