That sentence seems a bit awkward to me, too. I think we usually use と to connect nouns only. Here, 英語とフランス語の勉強をしたい + の forms some sort of noun (nominalizes) but 海外の友達を作りたい is a sentence. I guess that's why I feel it unnatural.
As you pointed out, this seems fine since two sentences are connected. I would say this way.
Two sentences are connected again. This is also fine.
Two nouns are connected and a verb したい follows. I think this is still OK, though 友達作り seems a bit formal and strict.
Here's the summary:
If you want to connect nouns only, you can connect them with と. If sentences only, connect them with して or たり. If their forms differ, unify them with one.
Although the sentence is indeed unnatural, I guess young Japanese tend to use this kind of words, especially on Twitter or something. I can take in the meaning at least.