1. 水泳が好きなので、よく大学のプールに泳ぎに行きます。運動にもなるし・・・。
Logically, is 水泳 the subject of なる?
Yes. The subject can be either 水泳 or the person's 泳ぎに行くこと.
2.
二つ上の兄
4つ下の妹
(I mean, it doesn't mean two older brothers and four younger sisters?)
Never. ひとつ、ふたつ、みっつ、よっつ... are never used for counting persons. It means age.
3. ところで足立さんって、一人っ子ですか。
For instance, is there much difference compared to 足立さんは?
Not really, just 足立さんって sounds more casual って used in colloquial context.
縺」縺ヲ・サ譬シ蜉ゥ菫ょ勧邨ょ勧・ス縺ョ諢丞袖 - 蝗ス隱櫁セ樊嶌 - goo霎樊嶌
って
[係助]名詞、名詞的な語に付く。
1 ある事柄を話題として取り上げて示す意を表す。…は。…というのは。「あなた―親切な人ね」「彼―だれのこ と」
4. 僕の場合は妹と5つちがいなんですけど
My translation: "In my case, my sister is five years different (in age) from me".
Is this correct? (It is the 5つちがい that I am not totally certain about.)
Yes, your interpretation is correct.
5. あ、そうですか。私、どういうわけか、学部の時から海外留学してた人って、一人っ子かなって思っちゃうんで すよ。だから足立さんも一人っ子かなって、思ったんですけど。
I think this means "I see. For some reason, I thought people who studied abroad from the time they were an undergraduate (might be) only children. So, I wondered if you were also an only child."
Is this right? Again, I am a bit unclear about the purpose of って in linking the two parts. Is the implication that the addressee studied abroad from the time he was an undergraduate?
Yes.