Se houver qualquer problema, a reunião pode ser remarcada para amanhã.

Houver is the future subjunctive form of haver.

After se when you mean if in a real future possibility, Portuguese often uses the future subjunctive:

• Se houver qualquer problema... = If there is / If there should be any problem...

Compare:

• Há um problema. = There is a problem.
• Tem um problema. = There is a problem. (common in spoken Brazilian Portuguese)
• Se houver um problema... = If there is a problem...

So há is present indicative, and tem is a common spoken alternative, but houver is the form that fits this conditional structure in more standard Portuguese.

It comes from the verb haver.

In this sentence, haver means to exist / to be in the sense of there is/there are.

Its future subjunctive forms are:

• se eu houver
• se você/ele/ela houver
• se nós houvermos
• se vocês/eles/elas houverem

In the sentence:

• Se houver qualquer problema...

there is no explicit subject like ele or você because haver here is being used impersonally, meaning if there is.

Because haver meaning to exist is usually treated as an impersonal verb in standard Portuguese.

That means it normally stays in the 3rd person singular, even if the thing after it is plural.

Examples:

• Há um problema. = There is one problem.
• Há vários problemas. = There are several problems.
• Se houver problemas... = If there are problems...

So even if you changed the sentence to:

• Se houver quaisquer problemas...

the verb would still be houver, not a plural form.

Here qualquer means any.

So:

• qualquer problema = any problem

This gives the idea of whatever problem might come up or any kind of problem.

You could also say:

• Se houver algum problema...

That is also very natural and common, and it means if there is some problem / if there is any problem.

A rough nuance:

• qualquer problema = any problem at all, whatever problem
• algum problema = some/any problem

In many situations, both work.

Because this sentence uses the passive voice.

• A reunião pode ser remarcada. = The meeting can be rescheduled.

Structure:

• pode = can / may
• ser = be
• remarcada = rescheduled

This focuses on the meeting rather than on who will reschedule it.

Compare:

• Podemos remarcar a reunião para amanhã. = We can reschedule the meeting for tomorrow.
• A reunião pode ser remarcada para amanhã. = The meeting can be rescheduled for tomorrow.

Both are correct, but the original is more impersonal and formal.

Because it agrees with a reunião, which is feminine singular.

In the passive voice, the past participle often agrees with the noun it describes when used with ser:

• o encontro foi remarcado
• a reunião foi remarcada
• os encontros foram remarcados
• as reuniões foram remarcadas

So in your sentence:

• a reunião = feminine singular
• therefore remarcada = feminine singular

Yes. Remarcar is a very common and natural verb for to reschedule.

Examples:

• Precisamos remarcar a consulta. = We need to reschedule the appointment.
• A aula foi remarcada. = The class was rescheduled.

Depending on context, you might also see:

• adiar = postpone
• transferir = move/transfer
• mudar a data = change the date

But for reschedule, remarcar is one of the most standard choices.

Here para amanhã means for tomorrow.

So:

• remarcada para amanhã = rescheduled for tomorrow

It indicates the new scheduled time/date.

It does not mean until tomorrow here.

Examples:

• A consulta foi marcada para sexta-feira. = The appointment was scheduled for Friday.
• A reunião foi remarcada para amanhã. = The meeting was rescheduled for tomorrow.

Yes, especially in everyday spoken Brazilian Portuguese.

A very common spoken alternative is:

• Se tiver qualquer problema, a reunião pode ser remarcada para amanhã.

Here tiver comes from ter, which is often used colloquially where more formal Portuguese might use haver.

So:

• Se houver qualquer problema... = more formal, more written, very standard
• Se tiver qualquer problema... = very common in speech, also natural in informal writing

Both are understandable and correct in their own contexts.

Because Se houver qualquer problema is an introductory conditional clause.

Portuguese normally separates this kind of clause with a comma when it comes first:

• Se chover, ficamos em casa.
• Se você quiser, eu posso ajudar.
• Se houver qualquer problema, a reunião pode ser remarcada para amanhã.

If the main clause comes first, the comma is often not necessary:

• A reunião pode ser remarcada para amanhã se houver qualquer problema.

The original sentence is already correct and natural, but it sounds a bit formal or administrative.

A more everyday version could be:

• Se tiver algum problema, a gente pode remarcar a reunião para amanhã.

Why this sounds more conversational:

• tiver instead of houver
• algum problema instead of qualquer problema
• a gente pode instead of the more impersonal passive pode ser remarcada

All of these are common in spoken Brazilian Portuguese.

Yes. Problema is a masculine noun:

• o problema
• qualquer problema

This surprises many learners because it ends in -a, but some nouns of Greek origin are masculine in Portuguese, such as:

• o problema
• o sistema
• o tema
• o programa

So in the sentence, qualquer problema is correct, not qualquer problema with a feminine article or adjective.