How much budget do I need....

[Silverobama]

I want to visit my friend in Singapore. She's been living there for many years. I want to stay there for month but I don't really know how much budget I need for the trip and stay. Would native speakers ask her something like "How much budget do I need if I want a monthly visit and stay?"

 

[emsr2d2]

I want to visit my friend in Singapore. She's been living there for many years. I want to stay there for a/one month but I don't really know how much budget money I'll need for the trip flight and a one-month stay.

I don't see the relevance of the underlined sentences.
Note my other changes. "Trip and stay" is tautologous. The one-month trip is your stay in Singapore. If you're not including the travel costs to get there, you could just say "... how much money I'll need for my stay".

Would native speakers ask her something like "How much budget do I need if I want a monthly visit and stay?"

No.
How much money will I need for a one-month visit/stay?
What should my budget be for a one-month visit/stay?
How much money will I need?
Can you give me a rough idea of how much it'll cost me for a month?

Note that "a monthly visit" means "visiting once a month". You mean a "month-long stay".

 

[teechar]

As you can see, "how much budget" doesn't work. However, you can say "how much do/will I need to budget for a month's stay/visit?". In that, the word "money" is implied between "much" and "do".