If the Court would allow it, I would have this taken as a submission of a brief.
I feel it necessary to note that the Court has already ruled on the matter of the Speaker concluding debate on a bill by locking the thread, that ruling is linked to in the post I made before locking the thread in question (though it would seem questionable as to whether the petitioner has actually read it), it is clear that the Speaker enjoys the authority to do so and that the correct method for redress is recall, not to demand that the Court overturns its ruling because the petitioner dislikes it.
Further, I would note that the law and the Rules are not prescriptive at all regarding legislative procedure, legislative procedure is, due to its not being detailed in any authoritative document, almost entirely within the Speaker's discretion (excluding the motion for an immediate vote and specific matters where the legal code requires that a vote be expedited or immediate). The "regular procedure", and I am sure this will horrify the petitioner, is the regular because it is the procedure that the Speaker prefers not because it is mandated to be, and there are, as a result of that, numerous exceptions to it (treaties use the "legislative procedure", with formal debate and remain under the control of the Government, rather than being able to be moved and seconded at will, despite falling within the realms of motions that use the "non-legislative procedure", as they do not enact, amend or repeal a law; omnibus bills are usually granted exception from the standing procedure provision that their sponsor must have notified the Speaker in advance; extensions are granted to formal debate at sponsors' requests, despite no provision for such existing in the standing procedure; there are other examples, but I feel these have been too log already.)
Now to address the questions put earlier.
Can the Speaker of the RA refuse to schedule for a vote and/or refuse to permit formal debate on a proposed piece of legislation under the Laws and RA Rules?
I would submit that, broadly speaking, the answer is yes as the Rules state that the Speaker "may" schedule a vote, not that he must, leaving it within his discretion. The exception to this would be in the case of a successful motion for an immediate vote, which is contained within the Rules, for in the event of such the Speaker "must schedule a vote [...] to begin as soon as permitted by law", which would usually be immediately, though if it is an enactment, amendment or repeal it may be delayed slightly if a number of other such enactments, amendments or repeals are at vote.
On the matter of formal debate, the Court will not find anything helpful in either the law or the Rules relating to it, as it is part of the "legislative procedure" created by the Speaker, and I would suggest that it would be very odd for the Court to compel something that is entirely within the Speaker's discretion.
(I should note, I have confined this to addressing votes on pieces of legislation, but the law does contain cases, as mentioned afore, where certain motions must be voted on immediately or with expedited debate.)
Also, can the Speaker of the RA deny the standard process and make up the rules as he goes along? And if so, where in the Legal Code or RA Rules is this permitted?
In this case, I would note again that the "standard process" is essentially a construct of the Speaker's Office, and that variation of it is necessary for the legislative process to be reasonably effective. As to where in the law or the Rules this is permitted, it is in the Constitution, Article 2, clause 6, which affords the Speaker discretion where the Rules and law are silent, and they are silent on the matter of the "standard process" for Assembly business, this is supported by the Court's prior ruling on the Speaker's powers (that being the ruling on request of Blue Wolf which bears the most similarity to the present situation).
Also, would in not be technically unconstitutional in terms of violating due process and free speech to take actions that thwart the democratic process detailed in the Constitution?
I would address this in respect to free speech first, the Speaker's action (or, rather, the lack thereof) does not prevent the discussion of the bill in question, so submission that the Speaker has violated the freedom of Assembly members to discuss the bill is somewhat nonsensical, to myself at least.
In respect of due process, the Speaker has not taken any action to deny the only lawful mechanism to compel him to bring the bill to vote, a motion for an immediate vote, and, indeed, has reminded members of said mechanism, nor has he prevented what the Court, in its previous ruling, stated was the most apt mechanism for redress of grievances relating to exercise of discretion: recall. The Speaker has, therefore, not violated the right of Assembly members to due process, the failure of members to make use of processes open to them for redress is not the responsibility of the Speaker, but of themselves.
Thank you, your honours.
EDIT: to correct slight misquote.
EDIT2: if the Court would allow it, I would have this taken as a submission of a brief.
EDIT3: to add the above to the top of the post, but in bolder and larger text.