Learn English – Using ‘several’ and ‘some’

Both some and any are used with indefinite reference.

Some is used if the idea is restricted or limited in some way. Any is used if the idea is unrestricted or unlimited. Any applies to all or none; some applies to part.

The restriction may be a real one - There's some cheese in the fridge - or a psychological one, existing only in the mind of the speaker - Would you like something to eat?

Michael Lewis (1986.34), The English Verb, LTP: Hove.

Do you have any wine/water? - Unrestricted

Can I have some wine/water, please? - Restricted, a limited amount

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).