So is the lake in the middle of the Zelda 1 map Lake Hylia?

yup. And if you look, you can see that there's an island/dungeon in the middle of both of them (from Zelda 1, as well as OoT, TP, LTTP, and LBW).

Also, are the locations in Skyward Sword and Twilight Princess the same locations as their analogues in other Zelda games, just with different names (i.e. Eldin Volcano is Death Mountain, Faron Woods are the Lost Woods, Lanayru Desert is the Gerudo Valley area etc.)

Yup. It's a bit hazy, but they generally line up to the same areas. But IIRC the lake and desert areas are flipped. Which is an example of tweaking the geography to suit gameplay.

I honestly always thought that each game had a forest, desert, and mountain themed area, as well as a lake in order to incorporate the traditional gameplay elements of the series. It seems so obvious now that each game takes place in the same place.

Yup, about 70% of the geography lines up. Hell, even Wind Waker you can see the areas line up. With Dragonroost island being Death Mountain, and so on.

I like that Termina theory by the way.

Thanks. It's a bit controversial in the fandom. But I personally like it.