What is the ruling on urine splashing onto the arm or foot, and what needs to be washed from clothing, shoes, and socks? And can one wipe a wet hand over socks that have been splashed with urine?

Splashing of urine is not excused by the majority of scholars. However, if the feeling of it is merely a whisper (waswasah) or a doubt, it should be disregarded, as the default is the absence of impurity.

If you are certain that urine splashes have contaminated the body, garment, or sock, it is obligatory to purify it with water for prayer, as avoiding impurity is a condition for the validity of prayer.

It is not obligatory to purify socks or shoes if they are not intended to be prayed in.

If you wipe over an impure sock and the impurity transfers to your wet hand, it is obligatory to wash your hand.

What is prescribed if the impurity is in the area of wiping is to wash it first, then wipe over the khuff (leather sock). However, if the impurity is not in the area of wiping, the hand does not become impure by wiping, and it is obligatory to purify the khuff by washing the area of impurity in order to pray in it.