Learn Hardcore Japanese: sekaizyuu no tomodati to nihongo de kaiwa wo sitai desu. - I want to have conversations in Japanese with friends around the world.

The desire 〜たいです almost always refers to the speaker, so “I” is already implied.
Japanese tends to leave out anything that can be guessed from context as “unnecessary”.

If you really want to emphasize “I”, you can say:

私は世界中の友達と日本語で会話をしたいです。
(with some emphasis on I in contrast to others)

What does と mean in 友達と here? Is it “and” or “with”?

In this sentence, と after 友達 means “with”:

友達と会話をする = to have a conversation with a friend / friends

The particle と has several common uses:

X と Y = X and Y (as a list)
A と話す / 会話する / 一緒に行く = talk / converse / go with A

Here, 友達と is “(together) with friends” rather than “friends and …”. There is no second item in a list, so it can’t be “and” in the English sense.

What does で mean in 日本語で? Why isn’t it just 日本語会話をしたいです?

In 日本語で会話をしたいです, the particle で marks the means or medium of the action:

日本語で = in Japanese / using Japanese (as the language)
会話をする = to have a conversation

So literally: “I want to do conversation in Japanese.”

Using で to indicate the language is very common:

日本語で話す = speak in Japanese
英語で書く = write in English
中国語で質問する = ask a question in Chinese

You normally need で there.
日本語会話をしたいです sounds like “I want Japanese conversation” as a set phrase or course name, which is different.

Why is it 会話をしたいです instead of just 話したいです or 日本語を話したいです?

All of these are possible, but they have slightly different nuances:

会話をしたいです
- 会話 = “conversation” (a back-and-forth exchange)
- Emphasis is on having two-way conversations.
話したいです (from 話す)
- More general “I want to talk / speak”.
- It doesn’t explicitly highlight the idea of conversation being with someone else.
日本語を話したいです
- Literally “I want to speak Japanese.”
- Focus is on using the Japanese language itself, not specifically on conversing with friends.

Your original sentence:

世界中の友達と日本語で会話をしたいです。

specifically combines:

friends all over the world
in Japanese
having conversations (会話)

so it strongly evokes practicing Japanese by actually talking with people around the world.

Why is it 会話をしたいです and not 会話したいです? Is there a difference?

Both are grammatically correct:

会話をしたいです。
会話したいです。

会話をする is the full expression (“to do conversation”), where 会話 is a noun and する is “to do”.

In casual speech, many people drop the を:

会話する → 会話をする (with を)
会話する → 会話する (direct)
会話したい → 会話したい (no を in between)

会話をしたいです sounds a bit clearer and slightly more formal/careful.
会話したいです is perfectly natural and slightly more compact; you might hear it in everyday speech.

Is したいです present or future? Does it mean “I want to” now or “I want to” in the future?

Japanese doesn’t sharply separate present and future the way English does.
〜したいです basically means:

“I want to do (it).”

It can refer to:

a current desire: “I want to do it (right now / these days).”
a future-oriented desire: “I want to (sometime / in general / in the future).”

Context decides the time nuance.

In your sentence:

世界中の友達と日本語で会話をしたいです。

it’s usually understood as a general or future wish:
“I want to (be able to) have conversations in Japanese with friends all over the world.”

Why is there no は or が for 友達 or 会話? Shouldn’t something be the subject?

The main grammatical markers here are:

友達と – “with friends” (と = with)
日本語で – “in Japanese” (で = by means / in)
会話を – direct object (を = marks what you “do”)
したいです – “want to do”

The subject (I) is omitted, as discussed earlier, and 会話 is clearly marked as the object by を, so no は or が is needed.

You could rephrase with は or が, but it slightly changes the nuance:

世界中の友達とは日本語で会話をしたいです。
(putting mild contrast/emphasis on the “with friends around the world” part)

However, in the basic sentence:

世界中の友達と日本語で会話をしたいです。

everything is already marked clearly by と, で, and を, so no subject/topic marker is necessary.

Is 友達 singular or plural here? Does it mean “a friend” or “friends”?

Japanese doesn’t usually mark singular vs plural the way English does.

友達 can mean:

a friend
friends
friend(s) in general

In 世界中の友達, the combination with 世界中 (“all over the world”) strongly suggests plural in natural English:

“friends all over the world”

If you really wanted to stress the idea of “many friends”, you could say:

世界中のたくさんの友達 = many friends around the world
世界中に友達がたくさんいます。 = I have many friends around the world.

But in most contexts, 世界中の友達 will be understood as plural.

What’s the difference between 世界中の友達と and 世界中の友達と一緒に?

Both can be translated as “with friends all over the world”, but there’s a nuance:

世界中の友達と日本語で会話をしたいです。
- Straightforward: “I want to have conversations in Japanese with friends all over the world.”
世界中の友達と一緒に日本語で会話をしたいです。
- 一緒に literally means “together (with)”.
- It emphasizes the sense of doing it together with them, sometimes adding a slight nuance of companionship or doing it as a shared activity.

In English, both often end up as “with friends all over the world”, but 一緒に adds a softer “together-ness” feeling, which is optional.

Could you also say 会話がしたいです instead of 会話をしたいです? What’s the difference?

Yes, both are possible:

会話をしたいです。
会話がしたいです。

The difference is subtle:

〜をしたい: treats 会話 as the direct object of “do”; fairly neutral.
〜がしたい: treats 会話 as the thing you want; sometimes feels a bit more like “I crave / really want conversation.”

So:

世界中の友達と日本語で会話をしたいです。
= I want to (do) conversations in Japanese with friends all over the world. (neutral)
世界中の友達と日本語で会話がしたいです。
= I really want conversations in Japanese with friends all over the world. (slight emphasis on the desire for conversation)

In everyday conversation, both are natural; the sentence with を is a bit more textbook-like, the が version can sound a little more emotional or personal depending on intonation and context.

Is 〜たいです polite? When would I drop です and just say 〜たい?

〜たいです is the polite form.
〜たい by itself is casual.

Polite:
- 世界中の友達と日本語で会話をしたいです。
  (what you’d say to a teacher, someone you don’t know well, in class, etc.)
Casual:
- 世界中の友達と日本語で会話したい。
  (what you’d say to close friends, family, people your age in an informal setting)

Use 〜たいです in most formal or neutral situations, especially if you’re not sure about the relationship or level of politeness expected.
Use 〜たい with people you already speak casually with.