What are the complete sentences? You have nonstandard grammar here unrelated to your word choice concern:
Is it too broad { to ask | to be asking | *in asking } about an unlimited number of subjects?
Second, the word illimited doesn't exist in standard English. (Which is not to say a native speaker wouldn't use it; it's definitely nonstandard though.) The Merriam-Webster's online dictionary evidently has an entry for this word in their unabridged version. Nothing in www.oxforddictionaries.com. Even if this was once a word, it is no longer a "living" word.
Are you, by chance, translating this from another language? Spanish evidently has illimitado; the English counterpart is unlimited. The prefix doesn't translate directly. Do not guess at English based on similarities; people won't understand you, or worse, you can hit upon a word that has a meaning you don't intend.
Although "limitless" and "unlimited" fit here grammatically (and are practically synonyms), you have a semantic problem. The sentence isn't sound.
You cannot actually speak about a limitless number of subjects. If you stop speaking, then you have thereby put a limit on how many subjects you spoke about. If you speak all day about four hundred subjects, until you are exhausted, then that was your limit.
A limit is some rule or obstacle which stops you from speaking about any number of subjects you want. The limit comes either from you, or it is externally imposed.
A sentence like "his ability to talk about just about anything seems limitless" makes sense. On the other hand, "can I say a limitless number of things to you" is comical; it would have been a good line for Peter Sellers' character in the 1968 film, The Party.
Essentially, you cannot be inquiring about a limit, when you're referring to a limit that comes from yourself! And in a sentence like "can I speak about an unlimited number of subjects", and related sentences of the same sort, "unlimited" has the interpretation of "not limited by me: I intend to speak on and on until I drop from exhaustion".
If you are inquiring about an imposed limit, it is much better to directly ask what the limit is:
How many subjects can I ask about, before the question is considered too broad?
What constitutes "too broad"? How many subjects can I ask about?
{ Is there | Does there exist } { a | some } limit on the number of subjects that I can ask about which is considered too broad? If so, what is the limit?
Note: can use such sentences like "can I say an unlimited number of things" if it is clear from the prior context that you're talking about an outside limit.
Humorous conversation:
A: Can I say an unlimited number of things?
B: I hardly think so; you will get hungry and tired, and then stop, thereby reaching your limit.
A: Haha! No, I mean, is there a limit on how many things I can talk about in this speech, or can I say an unlimited number of things?
B: Ah, now that you spoke properly, I can stop pretending I didn't understand! Yes, you can speak about a maximum of three topics.