Waswasas and doubts

Q: At the time of flushing the toilet at home, a number of drops splashed out from the toilet on to the toilet floor. Having stepped on these drops, I walked in the house and then walked outside in the same slippers. The ground outside was wet in patches as it had been raining. I then accidentally stepped in a muddy puddle with the same slippers. This caused water to seep through my leather and cotton socks with some moisture getting on to my feet. Before stepping on to the Masjid carpet, I removed my slippers, both pairs of socks and stepped on to the carpet. Some moisture passed from my feet on to the carpet. I walked through the carpeted masjid and went to the Wudhu area and washed my feet. In addition I carefully left my leather socks on the carpet before proceeding to the Wudhu Khana. They were wet from having stepped in the puddle but I tried to be careful not to put the wet part of the leather socks on the Masjid carpet, but now I am having a doubt as to exercised sufficient caution in this matter, i.e. there is a distinct possibility that the wetness on the leather sock went on to the carpet. Is the Masjid carpet which I walked on paak to perform Salah on or do I have to undertake the difficult task of informing the Masjid to wash the carpet?

Travelling with a mahram

Q: My mum wishes to travel to Zambia for a period exceeding 14 days. She will be staying with her friends (all woman). My mum is 67 years old. I've told her I will accompany her during her journey i.e from Johannesburg to her destination drop her off and do the same for her return journey. Please advise if this is acceptable?

Making a bequest for zakaat to be discharged and interest to be disposed off

Q: In the last will and testament of the deceased, it is instructed that the whole balance on one of the bank accounts of the deceased be deemed undischarged Zakaat and the whole balance on another bank account be deemed interest received and the two balances be disposed with in accordance with Shariah. Would the deceased’s instructions be tantamount to a bequest and consequently can only be limited to one-third of the gross value of the estate and, if so, what, if the total of the two balances and other bequests made exceed one-third? Please clarify.

Hitting children

Q: I wanted to know that in which case hitting you own child or ustaad hitting a student becomes permissible? Lets say an ustaad has a student and if that student misbehaves or does an action which is total disrespect or doesn't follow ustaads instructions despite that ustaad keeps advising him apprehending and admonishing him (ustaad knows he has won the child's heart already and ustaad knows if he hits the student then the student will take that hiding in a positive way he is a student that wont have an aversion for deen after he gives it to him) he doesn't come right and then the ustaad feels the only solution in his case will be hitting him with justice so now will hitting him be allowed and permissible?