Mimo deszczu nasza wycieczka w góry się udała.

Because mimo requires the genitive case.

• base form: deszcz = rain
• genitive singular: deszczu

So:

• mimo deszczu = despite the rain

This is something you simply need to learn with the preposition mimo: it is followed by the genitive.

Mimo means despite or in spite of.

So mimo deszczu means despite the rain.

You can also say pomimo deszczu. The meaning is basically the same, but:

• mimo is very common and neutral
• pomimo can sound a little more formal or emphatic

In everyday Polish, mimo is often the more natural choice.

Because w góry expresses direction / destination: a trip to the mountains.

With w, Polish often uses:

• accusative for movement toward somewhere
• locative for location in a place

So:

• w góry = to the mountains
• w górach = in the mountains

Here, wycieczka w góry is the normal expression for a trip to the mountains.

Because in Polish, the idiomatic phrase is wycieczka w góry.

Even though English uses to in a trip to the mountains, Polish does not normally say wycieczka do gór in this context. That would sound unnatural.

So this is a good phrase to learn as a whole:

• jechać w góry = to go to the mountains
• wycieczka w góry = a trip to the mountains

Because the subject is wycieczka, and wycieczka is a feminine noun.

In the Polish past tense, the verb agrees with the subject in gender and number.

So:

• udał się = masculine singular
• udała się = feminine singular
• udało się = neuter singular
• udały się = non-masculine personal plural
• udali się = masculine personal plural

Since nasza wycieczka is feminine singular, the correct form is udała się.

Here udać się means something like:

• to turn out well
• to be successful
• to go well

So wycieczka się udała means the trip was successful / the trip went well.

The się is part of the verb expression udać się. You should learn it as a unit, because:

• udać by itself usually means something else, such as to pretend or to imitate
• udać się has the meaning to succeed / turn out well / manage

So in this sentence, się is necessary.

It can be used in two very common ways.

1. About events, plans, attempts, jokes, meetings, trips, etc.
It means to be successful / go well.

Examples:

• Impreza się udała. = The party was a success.
• Plan się udał. = The plan worked.
• Wycieczka się udała. = The trip went well.

2. About a person managing to do something
It means to manage to.

Example:

• Udało mi się znaleźć klucze. = I managed to find the keys.

So yes, it can be used both for events and for people, but the structure is different.

No, Polish word order is fairly flexible.

Your sentence is grammatical, but other orders are also possible, for example:

• Mimo deszczu nasza wycieczka w góry udała się.
• Nasza wycieczka w góry udała się mimo deszczu.

The basic meaning stays the same, but the focus changes slightly.

For example:

• Mimo deszczu at the beginning highlights the contrast: despite the rain...
• putting mimo deszczu at the end can make it feel like an added detail

So the sentence is not locked into one single word order.

Yes, both are possible.

In Polish, się is a clitic, so its position is somewhat flexible, although it cannot normally stand at the very beginning of the sentence.

So you may hear both:

• wycieczka się udała
• wycieczka udała się

Both are correct. In many contexts, udała się may sound a little more neutral or natural to some speakers, but się udała is also perfectly acceptable.

This is one of those places where exposure to real Polish helps a lot, because clitic placement is guided partly by rhythm and emphasis, not only by strict rules.

Yes. That is also natural, but it is not exactly the same structure.

• nasza wycieczka w góry się udała = our trip to the mountains turned out well / was successful
• nasza wycieczka w góry była udana = our trip to the mountains was successful / was enjoyable / was a good one

The difference is small. In many contexts they are very close.

A useful distinction is:

• udała się focuses a bit more on the outcome: it worked out well
• była udana describes the trip as a successful or enjoyable experience

Both are good Polish.