Gender neutral term for family members who are all first born?
Speaking from personal experience (as a 長孫 on my paternal side):

老大 would be the most common gender-neutral term used within the family. Very common.

長子 can refer to the one oldest child of brothers and sisters, but there is quite a lot of variation in use between families, and can refer to the "eldest son" or the "eldest child". To be clear, I'd often go with "長子長女" as a phrase.

A more neutral circumlocution would be 最大的 which is spans formal and informal, in-family and out-of-family use. It defaults to referring to age (not height / width!), but if you want to be specific, you can use 年紀最大的 with "age" included.

There isn't any two-syllable word for the youngest that my family uses, although 老小 and 老幺 I have now seen on searching the Internet. 最小的 is the usual gender-neutral way of expressing it.