Do acts other than the declaration of faith and prayer establish a non-Muslim's conversion to Islam?

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Other pillars of Islam, specifically Zakat (obligatory charity), Sawm (fasting), and Hajj (pilgrimage), do not establish the conversion of an unbeliever to Islam. This is because pagans used to perform Hajj during the time of the Prophet, peace be upon him, until the Prophet forbade them from doing so, stating, "No polytheist shall perform Hajj after this year." Zakat is a form of charity, and pagans already give charity. Furthermore, the Christians of Banu Taghlib were subject to double the Zakat rate imposed on Muslims without becoming Muslims thereby. Fasting is merely abstention from specific actions during specific times, which is something a disbeliever may coincidentally undertake, and intent regarding fasting is an internal matter unknown to us.