Are giving gifts, kind treatment, using the siwak, maintaining kinship ties, and asking for prayers considered a custom or an act of worship, and can riya' (showing off) or minor shirk enter into them? And what are the books that address these issues?

Imam Al-Qarafi distinguished between showing off (riya') in acts of worship and associating other intentions (tashrik) with them. Riya' is performing an act of worship for the purpose of being glorified by people, or to attain benefit from them, or to avert harm from them. This is forbidden and invalidates the action.

As for tashrik, such as someone who fights in jihad for the obedience of Allah and to obtain spoils of war, or performs Hajj for trade, or fasts for their health, or performs ablution (wudu') for cleanliness along with the intention of worship—this does not invalidate the action nor does it render the doer sinful. Rather, they may even be rewarded, because the Lawgiver encouraged these benefits. And riya' only applies to what is seen or observed, such as seeking the glorification of creation.

These worldly objectives, when mixed with worship, may diminish the reward, but they do not invalidate the act of worship. And intending to gain people's affection through a gift, or to clean one's mouth with a miswak, or to speak kindly, is not considered riya'; rather, these are legitimate interests. Riya' is specific to righteous deeds. So, whoever performs worldly actions to be praised by people is not considered a show-off (murai).