Are there rituals (including vrat, tapa, japa, anusthan, purasharan,etc) through which one can fulfill one's wishes and overcome obstacles?
Fasting for Ekadasi vrata on both the light and dark fortnights of a month is said to fulfill all one's desires. Source: https://www.salagram.net/ekadasi-vratHBV.htm
- Citing from Chandogya-upanishad, chanting AUM/OM fulfills ones desires.
तद्वा एतदनुज्ञाक्षरं यद्धि किंचानुजानात्योमित्येव तदाहैषो एव समृद्धिर्यदनुज्ञा समर्धयिता ह वै कामानां भवति य एतदेवं विद्वानक्षरमुद्गीथमुपास्ते ॥ १.१.८ ॥
tadvā etadanujñākṣaraṃ yaddhi kiṃcānujānātyomityeva tadāhaiṣo eva samṛddhiryadanujñā samardhayitā ha vai kāmānāṃ bhavati ya etadevaṃ vidvānakṣaramudgīthamupāste || 1.1.8 ||
That akṣaram [Om] stands for assent. A person says Om whenever he wants to say yes. This Om is the key to progress. He who worships Om as the udgītha [Brahman], knowing it thus [as the fulfiller of all desires], has all his desires fulfilled.
- Citing from Shiva Purana which simply states to recite Rudra Samhita 3 times before the image of Bhairava: