"Mennäänkö uimahalliin?" The 1st person plural (we) form in colloquial Finnish is identical to passive, i.e. me mennään 'we go' compare: mennään 'one goes'. Now, when the subject is previously known (as probably in this case), the personal pronoun can be dropped in Finnish. This, of course, makes the passive and 1st person plural form identical as the use of the pronoun is the only difference between the two forms. In suggestions, such as this one here, the pronoun is usually dropped. (This sentence sounds like 'shall we/let's go to the swimming pool") As for your other concerns.. using passive or passive like constructions for 1st person plural is not as uncommon as you might think (the French say "on va", the Brazilians say "a gente va" etc.). Menemmekö is not a possible form as this is clearly a spoken/everyday sentence and not from a novel or newspaper. The -mme form is only used in formal written texts and is as good as obsolete in modern (colloquial) Finnish. The 'me + passive form' construction has pretty much replaced the -mme. Lastly, a word of warning - saying "meneMME" (instead of me mennään) in an everyday conversation makes you sound either non-native or douchy depending on the context and your level of Finnish. So, learn your passives well and use them to your heart's content! :)

Do you mean "se" instead of "hän"? I should come and get to know your real live speech.. These books are noo good!

"Menemmekö" would be grammatically correct, of course, but it sounds rather formal and is usually reserved for written language and official situations. Finnish people love to change things up for spoken language to make it more casual (like how we often refer to people as "it" instead of "hän") and so the passive is used in spoken language in the place of the normal 1st plural form.