Pros and Con-gnates

On balance, I'm not sure whether it's easier to learn a language in the same family (like German and English) or if it's easier to jump to a different branch of the tree and start learning, say, a Slavic language. Specifically, I'm thinking of how cognates, and even more specifically, "homophonic cognates" (which I'm quite sure is not a term) and Denglisch hinder and/or aid in understanding and attaining fluency in a language. German and English have many cognates (words which share a similar root), a simple example of which would be "finger." As is obvious, however, "finger" is also spelled the same in German and English and is pronounced almost identically (this is what I mean by a "homophonic cognate"). Furthermore, German and English also borrow many of the same words from French, Greek, and especially Latin, for example "religion" and "restaurant."

One must also contend with Denglisch, which is the bastardization of the two languages. Germans might say, for example, that they just "gedownloadet"something.

My point with all this is that while phenomena like Denglisch, common borrowings, and homophonic cognates can all make understanding a foreign language easier (especially in the beginning) because many words look and mean the same thing in the mother tongue, they can also make speaking more difficult and unsure (at least for me). The latter statement may sound paradoxical, but when so many words sound and mean similar things, it's easy to 1) say something correct but be unsure because it sounds made up, or 2) just conjure a new word out of thin air that somehow sounds German but is nowhere in the canon. Both can hinder truly mastering a language.

Thus I wonder if it might be easier to learn a language that has very little relationship to one's a mother's tongue when thinking only in the context of the phenomena above (i.e. holding everything else equal). My guess would be that initially it would be far harder to learn, but that fluency would come more suddenly and perhaps even more quickly.

Surely we must consider the borrowing of the word "zeitgeist" from German to be an altogether positive thing, however, no?