The basic grammar books use the active indicative form of verbs for these two parts of speech but can the main verb be a form of the passive, subjunctive or even any participial form?
If I understand your question correctly, any verb form of any verb that is followed by indirect statement may be followed by indirect statement regardless of the syntactical function otherwise of that verb. So…
Dicimus nos adesse, We say that we are present.
dicamus nos adesse, Let’s say that we are present.
dicentes nos adesse, saying that we are present.
dicere nos adesse, to say that we are present.
Real Latin syntax is mix and match and can throw practically anything at you, unlike the didactic compartmentalization that primers tend to use. A sentence like “Crediderunt nos esse qui dixisse deberemus nos adesse” is not out of the realm of possibility. That’s supposed to say “They believed that we were the ones who ought to have said that we were present.” That’s an awful sentence, but no more awful than some of the real Latin out there… 
I’m not sure I understand the question (I don’t think you mean parts of speech), but indirect speech can perfectly well be introduced by a verb in the passive (e.g. dicitur), or in the subjunctive (e.g. nemo dicat), or by a participle (though a participle is not a main verb). Basic grammar books just like to keep things simple, so as not to confuse you.
(just as both Barry and I, who wrote independently, used the verb dicere to introduce indirect speech. But I doubt that any real Latin out there is quite as awful as Barry’s made-up sentence. And don’t be fooled into thinking that Latin “can throw practically anything at you.” That’s like saying that Latin has practically no syntax. It has plenty!)
Vera, magister optime, dixisti.
As for “practically anything,” just a bit of hyperbole to make the point. But I’m sure SPQR got that.
Thanks for the input. Things are clear now. Is that “awful” sentence provided by Barry an example of what I will experience as I get into more advanced Latin? Actually I found the sentence amusing.
Yes, I wrote that somewhat tongue-in-cheek, and you took it as intended. What you do see are fairly long and complicated sentences or even paragraphs in indirect statement, such as happens several times in Book 1 of the De Bello Gallico (where Caesar doesn’t really cooperate with being the the relatively easy first author he is supposed to be). So, paratus es!
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