Any and some can be synonymous; that is, they may have the same meaning. Both may be used in affirmative or negative questions:
Examples: Will you have any?
Will you have some?
Won’t you have any?
Won’t you have some?
However, use some, not any, for affirmative statements and answers.
Correct Example: You may have some. Yes, I’d like some.
Incorrect Example: [...]

Although, traditionally, can has meant “to be able” and may has meant “to be permitted” or to express possibility, both can and may are commonly used interchangeably in respect to permission.
Example: He can hold his breath for 30 seconds.
Meaning: He is able to hold his breath for 30 seconds.
Example: He may hold his breath for [...]

What is a gerund and why do you need to know? Maybe it would be better to answer the second part of the question first so that you have some motivation to identify gerunds. If you are able to pick the gerund(s) out in your sentence, you will avoid a grammar gaffe that often goes [...]