Я надеюсь, что мы когда-нибудь поедем к морю вместе.

Because the verb is надеяться, which means to hope. It is a reflexive verb, so its forms include -сь / -ся.

The 1st person singular form is я надеюсь = I hope.

A few useful forms:

• я надеюсь
• ты надеешься
• мы надеемся
• они надеются

So надею is not a correct form of this verb.

Yes. Russian often drops subject pronouns when they are clear from the verb form.

So both of these are natural:

• Я надеюсь, что мы когда-нибудь поедем к морю вместе.
• Надеюсь, что мы когда-нибудь поедем к морю вместе.

Including Я makes the subject a little more explicit. Omitting it often sounds more natural in everyday speech.

Что introduces the clause after надеюсь and means that in this sentence.

So the structure is:

• Я надеюсь = I hope
• что мы когда-нибудь поедем к морю вместе = that we will someday go to the sea together

In English, that is often optional: I hope (that) we...
In Russian, что is very common and standard here.

Because что starts a subordinate clause.

Russian punctuation normally separates the main clause from the subordinate clause with a comma:

• Я надеюсь, что...

This is much more regular in Russian than in English. Even when English might omit a comma, Russian usually keeps it.

Here когда-нибудь means someday, one day, or at some unspecified time in the future.

It is a very common word in hopeful or uncertain future statements:

• когда-нибудь я выучу русский = someday I will learn Russian

A useful comparison:

• когда-нибудь = sometime in the future, someday
• когда-то = at some time, often once or at one time, and it can refer to the past

So in this sentence, когда-нибудь is the natural choice because the speaker is hoping about the future.

Поедем is the future form of the perfective verb поехать, and it fits a planned or hoped-for future trip.

Here it means something like we will go or we will make the trip.

Compare:

• мы поедем = we will go / we will set off
• мы едем = we are going / we are on our way / sometimes we are going soon
• мы будем ехать = we will be traveling (focus on the process)

In this sentence, the speaker is talking about the whole trip as a future event, so поедем is the best choice.

Because ехать / поехать means to go by transport: by car, train, bus, plane, and so on.

Russian distinguishes between:

• идти / пойти = to go on foot
• ехать / поехать = to go by vehicle/transport

A trip to the sea is normally imagined as travel by transport, so поедем sounds natural.

К takes the dative case, so море becomes морю.

• dictionary form: море
• dative singular: морю

So:

• к морю = to the sea / toward the sea

This is a good basic pattern to remember:

• к брату
• к сестре
• к дому
• к морю

Both can be possible, but they are not exactly the same in feeling.

• к морю means to the sea / toward the sea
• на море often means to the seaside, especially in the sense of going there for a holiday or vacation

So:

• поехать к морю = go to the sea, with the sea as the destination
• поехать на море = go to the seaside/on a sea vacation

In this sentence, к морю sounds slightly more literal or poetic, while на море would also be very common in everyday Russian.

Yes, it can move. Russian word order is flexible.

Here вместе at the end sounds natural and gives a small emphasis to together:

• Я надеюсь, что мы когда-нибудь поедем к морю вместе.

Other possible word orders include:

• Я надеюсь, что мы когда-нибудь вместе поедем к морю.
• Я надеюсь, что вместе мы когда-нибудь поедем к морю.

The original sentence is a very normal, neutral way to say it.

No, not completely. Russian word order is much more flexible than English word order, because case endings and verb forms carry a lot of grammatical information.

The given sentence is natural and neutral:

• Я надеюсь, что мы когда-нибудь поедем к морю вместе.

But Russian can rearrange parts of the sentence to change emphasis. For example, moving вместе earlier can emphasize the idea of being together, while moving когда-нибудь can highlight the uncertainty of someday.

So the sentence is not just grammatical; it also has a natural information flow: I hope → that we → someday → will go to the sea → together.