To what extent are the two hadiths "There are three whose prayers are not accepted and do not rise above their heads..." and "Whoever drinks alcohol, or falsely accuses a Muslim, or commits a sin during the daytime in Ramadan, their deeds will be nullified for the coming year" authentic, and does this mean that my prayers and zakat will not be accepted for a year if I commit these actions?

It is narrated in a hadith (definition) that the prayers of three types of people do not rise a handspan above their heads: "A man who leads people in prayer while they dislike his leadership, a woman who goes to bed while her husband is displeased with her, and two brothers who are in dispute." This wording is weak, but it is authentically narrated with the wording: "the runaway slave" instead of "two brothers who are in dispute." The commentators on the hadith explained that their prayers not rising means that they are not fully accepted, but they are still valid and fulfill the obligation, and they are not required to repeat them. So, the intention is that they are not fully accepted or do not ascend to God as a righteous deed, not that the action is useless. A Muslim is commanded to act, and their reward may not be multiplied or they may receive no reward if they are engaged in what is mentioned in the hadith.

As for the second hadith, it has not been found, but concerning alcohol, a hadith states: "Whoever drinks alcohol, his prayer will not be accepted for forty mornings." The meaning of non-acceptance of prayer here is the absence of reward, but the prayer is still valid. Deeds are only nullified by disbelief. However, committing sins does not nullify deeds if the conditions for their validity are met.

Slandering a Muslim is one of the major sins and has its punishment in this world. It has not been established that it nullifies deeds. The same applies to committing sins in Ramadan (definition). It is obligatory for whoever commits these prohibitions to repent to God and to be warned of His punishment. It is not permissible to abandon good deeds for fear of their non-acceptance after clarifying the meaning of non-acceptance.