According to the Gita, how do I abandon fruits of my karma? Should I donate my whole salary and stay hungry?

When you receive your salary at the month end, use ⅒ of it for Dharmic activities and the with the remaining amount, use it to keep your body in a fit condition for your sadhana and, to support your parents and other family members like your wife and children (if any).

nātyaśhnatastu yogo ’sti na chaikāntam anaśhnataḥ।

yuktāhāra-vihārasya yukta-cheṣhṭasya karmasu।

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Thanks for your question and asking me to answer!

न चाति स्वप्नशीलस्य जाग्रतो नैव चार्जुन || 6. 16||

So that way, you cannot abandon the fruits of your action. Now you will be attached to the action of donating all your money and staying hungry!

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You can as well stay hungry without earning! Why waste your time and energy in toiling from dawn to dusk just to earn money, donate all of them and stay hungry?

Abandoning the fruits of actions means you offer the results of your actions to God. This doesn't mean that you will not receive the fruits of your actions. You certainly will! But when you work, you must perform it as an offering unto God and leave the results in His hands. You don't think about the results of your actions while you are working, and even after you are done with your work!

युक्तस्वप्नावबोधस्य योगो भवति दु:खहा || 6. 17||

Do you think there will ever be a movie that features a line such as “You graduated at the top of your class in liberal arts, we need your help”?

yukta-svapnāvabodhasya yogo bhavati duḥkha-hā।। 6.17

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There must be a sense of balance in all your activities avoiding the two extremes of being a workaholic and being a lazy person. Similarly in your eating, sleeping, relaxing, you must be moderate.

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Nirvritananda

Is there any need of sweating so much just to stay hungry? And after so much toiling from morning till evening or night, where's the energy left in you to stay hungry even? You will not only be able not to stay hungry, but you will overeat! To stay hungry, your body must in a fit condition.

Says Sri Krishna in the 6th Chapter of the Bhagavad Gita —

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na chāti-svapna-śhīlasya jāgrato naiva chārjuna।। 6.16।।

O Arjuna! Yoga is not for him who eats too much or doesn't eat all; Yoga is not for him who sleeps too much or doesn't sleep at all

If you want to donate your whole salary and stay hungry, why work at all in the first place?

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युक्ताहारविहारस्य युक्तचेष्टस्य कर्मसु |

A person who is moderate in food, recreation, work, sleep and waking, to such a person Yoga becomes a means to kill sorrow!

नात्यश्नतस्तु योगोऽस्ति न चैकान्तमनश्नत: |

Would deporting illegal aliens alleviate the housing crisis?