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1.我拿到绿卡时30.5岁，Selective Service没有注册，听说需要索取一份status information letter。

-No in your case because you were more than 26 when you got the green card. Just explain it if asked.

为了证明自己的F1-H1B-GC身份，需要提供所有的I-20，H1B批准函和绿卡复印件么？

-You don't need to prove your non-immigrant status because that kind of status proof is used for green card application, not US citizenship applicaiton.
我8月中旬准备递交入籍申请，这个status information letter多长时间能批下来？

-Not need it.

2.我拿到绿卡后没有换SSN卡，入籍时F1时代的SSN卡会是个问题么？