第一天

今天iTalki开始的. 我回美国从北京了想要下去学中文.

I tried to say, "Today I started iTalki. I've returned to America from Beijing and would like to continue studying Chinese." How close did I get?

How about?

我已经返回美国从北京了，并希望继续学习中文。

第一天

今天iTalki开始的. 我回美国从北京了想要下去学中文.

I tried to say, "Today I started iTalki. I've returned to America from Beijing and would like to continue studying Chinese." How close did I get?

我从北京回到美国，我想要继续学中文

第一天

今天iTalki开始的. 我回美国从北京了想要下去学中文.

I tried to say, "Today I started iTalki. I've returned to America from Beijing and would like to continue studying Chinese." How close did I get?

Many corrections already - but let me give you a link:

http://resources.allsetlearning.com/chinese/grammar/Word_order

I from Beijing to America returned have

第一天

今天iTalki开始的. 我回美国从北京了想要下去学中文.

I tried to say, "Today I started iTalki.

今天开始（来）italki。same as in English！

I've returned to America from Beijing and would like to continue studying Chinese." 

我已经从北京回到美国了，想要继续学汉语。

A very good start！Although there are some tiny mistakes here and there，your sentences can still be easily understood by native Chinese speakers. Good job！

第一天

今天从iTalki开始的. 我从北京回到美国,我想继续学中文.

I tried to say, "Today I started iTalki. I've returned to America from Beijing and would like to continue studying Chinese." How close did I get?

You have some grammer mistake.But people can understand what you are talking about.I suggest that you can practise more about the grammer.That would be help.