"Shall I make something?"
Regarding the difference between なにか and なにも, I'll copy @KagayakuSeiza's example above and add to it.
どこ=where, どこか=somewhere; どこも = everywhere/anywhere (with a positive verb) or nowhere (with a negative verb)
いつ=when, いつか=someday; いつも = always, every time (with a positive verb) or never (with a negative verb)
だれ=who, だれか=someone; だれも = everyone/anyone (with a positive verb) or nobody/no one (with a negative verb)
And for your specific question:
なに = what; なにか = something; なにも = anything/everything (with a positive verb) or nothing (with a negative verb)
Or for more detailed instructions: https://www.tofugu.com/japanese/how-to-install-japanese-keyboard/
Sneaky, but I think they should do that a lot more, break them up, give them as individual characters, give similar looking blocks. I find it's too easy to grab the right card while only actually having learned the first character in a word. Being able to increase the difficulty as you go along would be great!
the difference between using ませんか？ and ましょうか？ is the expectation of the speaker. If someone is unsure of the response then they will probably use ませんか？... 「何かを作りませんか？」sounds like a soft invitation where the speaker doesn't know the answer, it's more polite and less direct, "do you want to make something?"... while「何かを作りましょうか？」it's more like the speaker knows the answer and is trying to give it a push, "shall we make something?" in English is a good translation for this feeling.
also「何かを作りましょうか？」can be translated to both "Should I make something?" and "Should we make something".
To make the plain volitional form, you change the last う sound to an おう for godan verbs, and for ichidan verbs you get rid of the る and add よう。From there you add か to make it a question (shall I). For example, 作る would become 作ろう、as it is a godan verb, but 食べる would become 食べよう、as it is an ichidan verb.
Another poster challenged the use of 「何かを」but then deleted their comments and my replies. There are other comments on this page which also express some confusion about this construction.
For reference, 何か is a collocation which acts as either a pronoun or adverb, and can be used either with or without particles such as を and が depending on how it is used.
Here are some colloquial examples of the「何かを」construction:
1) 何かをやるのに遅いということは決してない A book on Amazon Japan from an established publisher
2) 君が何かを企んでいても A song by the idol group SMAP
3) 何かを作りたい！クリエイティブな芸術系の趣味１０１個まとめ A blog post
And here are links to two dictionary definitions, with further examples of 何か being used with particles:
The Jisho.org definition lists 何か as being an adverb only, however, on the same page one can see 何か being used with particles in phrases such as 「何かと言うと」.