Slingshots Slingshots

The plural from is more natural as a one-word title, especially since the body of your post describes the (many) slingshots of your childhood, not just one slingshot.

I remember my father once said that he could get a home-made gun for me, but he didn't do that never ended up doing the endat. I remember my father once said that he could get a home-made gun for me, but he never ended up doing that.

At that time, China [hadn't controlled | hadn’t started to control | didn’t control] guns so / as strictly as now, so gasair guns could be bought in some shops. At that time, China [hadn't controlled | hadn’t started to control | didn’t control] guns so / as strictly as now, so air guns could be bought in some shops.

We call them air guns, even though some of them do use a compressed gas such as carbon dioxide.

I only had slingshots [made by myself | I made myself | homemade slingshots]. I only had slingshots [made by myself | I made myself | homemade slingshots].

“By myself” emphasizes that nobody helped you make them. This isn’t incorrect, but it would be more natural to simply say you made them yourself (without “by”) or to describe them as “homemade.”

When I was a child, I loved to play with slingshots. When I was a child, I loved to play with slingshots.

“Slingshot” is not the name of a game or a musical instrument, so you need “play with” instead of just “play.”

When I was a child, I loved to play with slingshots. When I was a child, I loved to play with slingshots.

When I made a slingshot, I'd use a y-shaped tree branches, rubber bands and an oval piece of leather. When I made a slingshot, I'd use a y-shaped tree branch, rubber bands and an oval piece of leather.

Although I [didn't shoot down a few] birds, slingshots brought a lot of joy to my childhood. Although I [didn't shoot down a few] birds, slingshots brought a lot of joy to my childhood.

“Didn’t shoot down a few” isn’t incorrect, but it’s a form of double-negative (“not a few”), so it’s ambiguous: “not a few” usually means “not just a few,” i.e., “many,” although it can be literally interpreted as “less than a few.” I understand “didn’t shoot down a few” to mean you shot very many birds, but I’m not sure this is what you intended to say.

Although I didn't shoot down a few birds, slingshots brought a lot of joy to my childhood. Although I didn't shoot down a few birds, slingshots brought a lot of joy to my childhood.

I'm not sure how "I didn't shoot down a few birds" fits in.

Although I didn't shoot down a fewny birds, slingshots brought a lot of joy to my childhood. Although I didn't shoot down any birds, slingshots brought a lot of joy to my childhood.