Learn Romanian: Satul este într-o vale frumoasă. - The village is in a beautiful valley.

The preposition în (in) merges with the feminine indefinite article o (a) to prevent vowels from clashing and make speech flow faster. An extra -tr- sound bridges them together. For masculine or neuter nouns, you would use într-un.

The word vale ends in "-e". How can I tell what gender it is to match the adjective?

Nouns ending in -e are tricky because they can be masculine, feminine, or neuter, so you often just have to learn them as you go. Vale is feminine (singular o vale, plural două văi). Because it is feminine, it triggers the feminine article o and the feminine adjective form frumoasă.

Would it be wrong to change the word order and say într-o frumoasă vale?

It wouldn't be strictly wrong, but it would sound quite poetic, literary, or dramatic. In standard everyday Romanian, descriptive adjectives like frumoasă almost always come immediately after the noun they describe (o vale frumoasă).