If you daven for a parnasah and then just sit back will money come to you?
If I daven for parnassah, probably not. However, for someone righteous enough, maybe, but it can come with a catch.
Ta'anis 25a relates this story
אמרה ליה דביתהו עד אימת ניזיל ונצטער כולי האי אמר לה מאי נעביד בעי רחמי דניתבו לך מידי בעא רחמי יצתה כמין פיסת יד ויהבו ליה חד כרעא דפתורא דדהבא (חזאי) בחלמא עתידי צדיקי דאכלי אפתורא דדהבא דאית ליה תלת כרעי (ואת) אוכלת אפתורא דתרי כרעי (אמרה ליה) ניחא לך דמיכל אכלי כולי עלמא אפתורא דמשלם ואנן אפתורא דמחסר אמרה ליה ומאי נעביד בעי רחמי דנשקלינהו מינך בעי רחמי ושקלוהו תנא גדול היה נס אחרון יותר מן הראשון
Rabbi Chanina's wife asked him how much longer they would have to suffer in poverty, and she told him to pray for something to be given to them.
So Rabbi Chanina prayed, and a miracle occured - a hand appeared and gave him a gold table-leg.
Afterwards, he saw in a dream that in Olam Haba they would have a table with only two legs instead of the three-legged table that everyone else had. So he told his wife this and she made him give it back (which was a bigger miracle).
No, but if you work the minimum amount and devote yourself to the service of God more and more, then the amount of exertion that you will need to do will diminish down to zero.
If a man strengthens himself in the service of G-d, chooses to fear G-d, trusts in Him on matters of torah and matters of this world, steers away from bad things and desires good midot (character traits), does not rebel in times of plenty, does not turn towards leisure, does not follow his evil inclination, is not enticed by the witchery of this world - the burden of earning a livelihood will be removed from him, since the two reasons mentioned above no longer apply to him, namely, to test him on his choice and to see if he will rebel during prosperity. His livelihood will come to him without effort or difficulty, according to his needs, as written "G-d will not bring hunger to the righteous" (Mishlei 10:3).
I agree with YS and would add if u were at that level it would probably not fall from the sky, it will come in a way like finding money on the street or getting a raise/ promotion.
About good things falling from the sky - manna is the first that comes to mind; buew it was delivered without prayer.
Personally, I have not seen money fall from the sky; have you heard of such a thing?
When a person prays for money to fall from the sky, what might they be thinking of? If to enrich themselves in order to provide better for the family, then anything that happens suddenly and wholly unexpected, such as a surprise offer of a well paying job, then their prayer was answered.