Sepanjang jalan, saya menarik napas dalam-dalam supaya tetap tenang.

Sepanjang means along/throughout the length of something (often something with a “path” or “extent,” like a road, river, journey, time period). In sepanjang jalan, it’s all along the road / the whole way.
Selama is more purely about duration in time: for/during (e.g., selama dua jam = for two hours).

In sepanjang jalan, jalan most naturally means the road/way (the route). By extension it can also feel like the whole way / during the trip.
If you want to be explicit about the trip, you could say sepanjang perjalanan (throughout the journey).

It’s optional, but common when the sentence starts with an introductory phrase.
Sepanjang jalan, sets the scene (Along the way, ...). In Indonesian writing, a comma is often used here similarly to English.

Yes, often. If the subject is clear from context, Indonesian frequently omits pronouns:
Sepanjang jalan, menarik napas dalam-dalam supaya tetap tenang.
Keeping saya is clearer and more neutral, especially in written Indonesian or when you want emphasis.

Reduplication here intensifies/iterates the quality: dalam-dalam means very deep / deeply (repeatedly).
So menarik napas dalam = take a deep breath (could be one deep breath)
menarik napas dalam-dalam = take deep breaths / take a really deep breath (stronger, often repeated).

It primarily expresses purpose/intention: you take deep breaths in order to stay calm.
In context, it can also imply the expected result, but grammatically it’s framed as purpose.

Indonesian often uses adjectives after linking ideas like tetap without changing form. tenang functions as the state/condition: (to) remain calm.
If you wanted “calmly” as a manner adverb, you might use dengan tenang (calmly), but that would be a different structure/meaning.