Is each of the following considered shirk (polytheism) in intention and invalidates prayer: rushing through it due to waiting for others or fearing their mockery for prolonging prayer due to obsessive thoughts, or being careful not to wet the floor with water during ablution so as not to inconvenience others, or using a special prayer rug to avoid people's comments despite not minding praying on the ground?

Beware of obsessive whispers (waswas) concerning prayer, purification, showing off (riyaa'), and other matters, and do not pay attention to them. What was mentioned is not showing off; rather, you may be rewarded for it, such as your eagerness not to wet the ground to avoid harming people, your praying on a special prayer mat, and your sometimes hastening in prayer while being keen to complete it for a purpose. Indeed, the Prophet (peace be upon him) hastened his prayer upon hearing the crying of a child.