“But suddenly, the hard oxonium conjugated system is destroyed by the soft methanol base, in strong acidic conditions (HBr continues to generate, during reaction). The latter doesn’t sound well, at all.”
However, if you read carefully the operational protocol of the preparation of 2,5-dihydro-2,5-dimethoxyfuran that is described in the cited reference (notably: Organic Syntheses, 40, 29, (1960)), you will observe that the reaction does not occur under strong acidic conditions, due to the addition of a large excess of Na2CO3. Besides, I am not sure if the preparation of N-hydroxy-pyrrole could occur under alkaline conditions that furan ring opening, followed by pyrrole ring closure is very slow. Is it an one-pot reaction or not?
I think you are going way further than needed. I am presuming this is a typical kind of question posed to a student. The mechanism that I found seems simple enough for the assignment.
Re: acidity
t-Butyl bromide can be solvolyzed in a polar solvent without additional base being present. If the medium does become sufficiently acidic or if HBr were added, the reaction can be reversed. The problem specified did not mention how it was to be carried out, but rather the minimum information. Granted it had been a long time since I had seen the formation of a dihydrofuran, the intermediate indicated by the original poster seemed right and could reflect a reference found. Furthermore, I would be surprised if the reaction were to stop at the bromide in the absence of carbonate.
One can estimate the ease of solvolysis from the reverse reaction. For example, acetobromoglucose is also an Org Syn prep,
http://www.orgsyn.org/content/pdfs/procedures/cv3p0011.pdf.
You may examine the conditions and estimate the equilibrium from a mixture of HBr and methanol. Although I grant some bromide may exist, the conditions suggest solvolysis may be a quite easy reaction, especially as the bromide is used to prepare sugar derivatives.
Re: reaction with hydroxylamine
reaction were to stop at the bromide in the absence of carbonate.
One can estimate the ease of solvolysis from the reverse reaction. For example, acetobromoglucose is also an Org Syn prep,
http://www.orgsyn.org/content/pdfs/procedures/cv3p0011.pdf.
You may examine the conditions and estimate the equilibrium from a mixture of HBr and methanol. Although I grant some bromide may exist, the conditions suggest solvolysis may be a quite easy reaction, especially as the bromide is used to prepare sugar derivatives.
Re: reaction with hydroxylamine
Again, we should consider how the problem is written. I have used both hydroxylamine and its hydrochloride. Without searching, I don't think the free amine is commercially available, hence any indication of its use probably refers to the HCl salt. Clearly, the problem shows the reaction is a second reaction. Since the starting material is a dihydrofuran, the aromatic product does not follow from the indicated reaction. This would seem to be exactly what the poster was asking about. A solution to this dilemma is that a second equivalent of hydroxylamine is needed and it must operate as an oxidant.
Since the intermediate is an acetal, logically an acid may be required to open it for a reaction with hydroxylamine. Whether the hydrochloride present or residual HBr may be present, I don't know. None the less, I think the purpose of the poster was to attempt to write a mechanism, even if this may have required real or imaginary reagents. We sometimes have realize problems have been written with errors. Although this creates a problem for students, it can be helpful if someone with enough expertise can recognize this possibility. This is still just a mechanism question.