The moon and thousands of stars could be seen in the night sky.
It seemed like I could catch/touch them if I reached for them.
(1)There was the moon and were full of stars in the night sky. → The moon and thousands of stars could be seen in the night sky. または I could see the moon and thousands of stars in the night sky.
(2)It seemed like l could catch them if I reach for them. → It seemed like I could catch/touch them if I reached for them.
(2)の文章は「仮定法」の文法ですね。ですから「could ~ if +動詞の過去形」というパターンを使う必要があります。つまり、「reach」ではなく、「reached」(過去形)を使う必要があります。
例えば、
If I WERE rich, I COULD go on a trip around the world.
(もしもお金持ちであったら、世界一周旅に行けるんだけどね。)
The night sky was full of stars and the moon could be seen. It seemed like I could catch them if I reached out for them.
トラベルさんの文章はほぼあってますが最初の文章だけが”were”は少し違う使い方にになってます。構成として夜空を主語にした方が文章が書きやすくなります。後にくる夜空で言いたかったことが分かりますが、元の文章の”There was the moon and were full of stars”は月に星さんがいっぱいあるみたいな意味になってます。二番目の文章の”reach”は過去形にして仮定の文章ができます。