I have no friends to play with.
Hello,
As far as I understand, “Spielen” is used as a noum here? Would the literal translation be close to “I have no friend for the play(ing)”?
Also, would “Ich habe keine Freunde um zu spielen” be correct here?
Yes. It’s called “Nominalisierung” of verbs (the process of turning verbs into nouns; noun-ification). If you do that, you must write the word’s first letter in upper case.
No. “zum” is short for “zu dem”, therefore “zum Spielen” is short for “zu dem Spielen”. If you insist on a literal translation, it would be something like “I have no friend to the playing”. “for” means “für” and “zu” means “to”. If you insist on a literal translation, it would be some mixture of these two constructs. And that mixture “to the playing” does not exist in English. But if you’re less strict, you could maybe answer “kind of” instead of “no”.
Just like “I have no friends to play with” is short for “I have no friends with whom I can play”,
“Ich habe keine Freunde zum Spielen” is short for “Ich habe keine Freunde, mit denen ich spielen kann”. Notice that in one case “spielen” is in lower case (because it’s a verb), in the other case, it’s in upper case (because we “nominalized”/noun-ified the verb).
“to play with” is already the literal translation for the “Nominalisierung”. Maybe it’s not a literal word for word translation, but it’s what comes closest. You can’t always map a language one-to-one to a different language. That’s why they’re different.
No. This exists as a correct sentence, but has a different meaning. It sounds like “I don’t have money in order to pay the entry fee.” “I don’t have friends in order to play”.
Would the literal translation be close to “I have no friend for the play(ing)” ?
I would say yes. That would be a one-to-one literal translation of every component in the sentence (apart from one typo: friend → friends).
Of course, that’s not idiomatic english, and davidculley’s suggestions are more appropriate.
But sometimes literal translations help with understanding the other language’s grammar, at least if they are still within the limits of what your own language can do. Things get tough when you can’t explain some grammar construct even by literal translation. That’s when you need to build some intuition. The fun of learning languages!
Otherwise, everything else davidculley explained applies. 
So initially, I thought maybe zum was “um+zu”. It didn’t make all that much sense to me, since I had mostly seen zu+article (dative), but I thought maybe this was a special case…
Then, I realized that it was Spielen and not spielen so at this point, my “um+zu” hypothesis was definitely out the window.
I see… I did not even consider it, but now that you mention it, I can kind of see it 
Next, I checked in the dictionary and found that Spielen was indeed listed as a noun (das Spielen).
ChatGPT confirmed that zum was “zu+dem”, which made sense, but I asked about the literal translation to make sure I understood it correctly.
Of course, and from now on, I will mostly consider “zum Spielen” as a unit. (This makes me think of another example I saw yesterday: “Im moment”, which I assumed was a combination of in+diesem).
Indeed, I think they can help A LOT.
I don’t know about you, but I find that to be very rarely the case (except for idioms maybe) and when it does happen, then I’ll just switch to “unit/fixed expression mode”. I guess the “distance” between your native language and your target language would be a major factor here. I mean, if a concept simply does not exist in your native language, then I guess you’re pretty much… Well, out of luck
If you could think of a few German examples, I’d be very curious.
Very very interesting… I don’t know how you feel about it, but I’d actually argue that literal translations are a very good way to build that intuition and that in cases were a literal translation is impossible or not helpful, then I’d say it mostly becomes a matter of memorization.
What do you think?
And going back to our example, can this idea be applied to other “Nominalisierung”?
I see that das Lesen is also a noun, so could I say for instance:
Ich habe nicht genug Zeit zum Lesen?
I think it depends on what kind of learner you are. Some people just need enough examples, and be corrected enough times, to build an intuition. And some need explanations, the why and how, i.e. rules.
Personally, it helps me more to think like a native if I don’t treat certain features as black boxes, because then my understanding applies to more situations and sentence constructs.
I see that das Lesen is also a noun, so could I say for instance:
Ich habe nicht genug Zeit zum Lesen?
Yes! You can basically do that with every verb. In fact, it can be used not only with single-word verbs, but with whole phrases:
Zum Mitnehmen oder zum hier Essen? - Is this to eat here or to go? (Typical question when you buy a sandwich for example)
Ich bin nicht der Typ zum auf-den-Tisch-Hauen. - I’m not the type to pound the table. (dict.cc | auf den Tisch hauen | English Dictionary)
Mein Gott. Das ist ja zum auf-die-Palme-Gehen!! - My God. That’s so aggravating!! (dict.cc | auf die Palme bringen | English Dictionary)
I’m not even sure whether you write this with hyphens or not. It’s a spoken thing.
That’s perfect, thank you!