ryokou de totta syasin wo genzousitakute, sannenburi ni eki mae no syasinkan ni itta.

A natural way to parse it is:

• 旅行で撮った写真を
• 現像したくて、
• 三年ぶりに
• 駅前の写真館に
• 行った。

So the structure is basically:

• [the photos taken on the trip]
• because I wanted to develop them
• for the first time in three years
• to the photo shop in front of the station
• went

Japanese often puts a lot of information before the final verb, so it helps to identify noun phrases and modifiers first.

Here, で marks the situation / occasion / setting in which the photos were taken.

• 旅行で撮った写真 = photos taken on the trip / during the trip

This is not the で of location for an action like 学校で勉強する, although it is related in the sense of marking the context of an action.

You can think of it as close to:

• 旅行のときに撮った写真
• photos I took when I was traveling

So 旅行で here does not mean by means of a trip; it means in the context of the trip.

Because Japanese uses a relative clause before the noun.

• 撮った写真 = the photos that I took

English uses a structure like photos that I took, with the noun first and the explanation after it.
Japanese does the opposite:

• [I took] photos
• 撮った 写真

There is no word like that / which / who in Japanese here. The verb phrase simply comes directly before the noun it modifies.

Because 撮った shows that the photo-taking was a completed action.

• 撮った写真 = photos that were taken
• 撮る写真 would suggest photos that one takes / will take / tends to take, depending on context

In this sentence, the photos already exist, and now the speaker wants to develop them, so 撮った is the natural form.

Good question. With 〜たい, both を and が can appear with the thing desired.

So both of these can be possible in Japanese:

• 写真を現像したい
• 写真が現像したい

But を is extremely common and natural, especially with a direct object and an action verb like 現像する.

Here:

• 写真を現像したい = want to develop the photos

So 写真 is the object of 現像する, and たい is attached to that verb.

現像したくて is the て-form of 現像したい.

• 現像したい = want to develop
• 現像したくて = wanting to develop / because I wanted to develop

In this sentence, it gives the reason or motivation for the next action:

• 現像したくて、写真館に行った
• I went to the photo shop because I wanted to develop them

This use of 〜て often connects two actions when the first part explains the speaker’s reason for doing the second part.

Both can work, but they feel slightly different.

• 現像したくて、行った
  = I wanted to develop them, so I went
  This sounds natural and direct as a motivation leading to the action.

• 現像したかったので、行った
  = Because I had wanted to develop them, I went
  This is a bit more explicitly explanatory.

Even though the main verb is past, 〜たくて is fine because it describes the speaker’s desire at that time, which led to the action of going.

So this sentence is not ungrammatical or strange at all. It is a very natural way to express motivation.

In this sentence, the natural interpretation is have them developed.

Literally, 現像する means to develop film/photos, but Japanese often does not specify the agent as clearly as English does. Since the speaker goes to a 写真館, the practical meaning is:

• the speaker went there to get the photos developed

So the Japanese wording focuses on the act/result, while English often prefers to make the service nuance explicit with have them developed.

三年ぶりに means:

• for the first time in three years
• after a gap of three years

The pattern is:

• X年ぶりに + verb
• do something for the first time in X years

So here, it means the speaker went to that photo shop again after not going there for three years.

It does not just mean a duration of three years. It emphasizes the return after a long interval.

Because 三年ぶりに is functioning adverbially, modifying the verb 行った.

Compare:

• 三年ぶりに行った = went there for the first time in three years
• 三年ぶりの写真館 = the photo shop, seen again after three years / the photo shop after a three-year gap

So:

• 〜ぶりに modifies a verb
• 〜ぶりの modifies a noun

駅前 is a set compound noun meaning:

• the area in front of the station
• the station-front area

So:

• 駅前の写真館 = the photo shop by the station / in front of the station

By contrast, 駅の前 is a more literal phrase meaning the front of the station.

In many cases they are close in meaning, but 駅前 often sounds more like a place name or neighborhood area, while 駅の前 can sound more physically literal.

写真館 usually means a photo studio or a photo shop.

Depending on context, it can refer to a place that:

• takes portrait photos
• develops film
• prints photos

In this sentence, because of 現像, it is clearly the kind of place where you would take film or photos to be developed/printed.

It does not mean something like a gallery or museum of photographs.

Yes, the subject is omitted, but it is naturally understood as the same person throughout.

That person:

• took the photos
• wanted to develop them
• went to the photo shop

In English, we usually need to repeat I, but Japanese leaves it out when it is obvious from context.

Also, with 〜たくて, it is very natural for the person who has the desire and the person who performs the next action to be the same. So the sentence strongly suggests one continuous subject: I.