To refer back to "one or more", should I use "it" or "them"?
Solution 1:
I notice you are using the plural "packages" in all cases. The correct complement for the plural noun in that case would be "them".
I personally have no trouble with using "one or more packages" as "more" is closer to "packages" and "one or more package" would sound bizarre.
Moreover, I agree with RIMMER that "one" could be replaced. His suggestion of "you" might work, but may strike too informal a tone for software documentation. Instead you might try:
This option allows users to download one or more packages without installing them.
Solution 2:
Couldn't you avoid this problem by saying some packages, or just packages, as in
This option allows you to download packages without installing them.
It seems to me the one or more is rather superfluous, as nobody is likely to be interested in an option that allows you to download no packages.
Solution 3:
Firstly, I believe starting with This option allows you to would be a lot better in this situation, because obviously the document will be read by only 1 user at a time and it should be talking to this specific user, although your original idea is grammatically correct too.
As for the latter sentence, I am not sure which of those you proposed is correct, but again, I'd like to propose a better solution, at least in my opinion:
Download one or more packages without proceeding with the installation.
Which basically keeps the language on the "action" level and let's the user know that they can install the packages themselves later when they choose to.