Tahaarat

Doubting whether one is in the state of janaabat or not

Q: My question is regarding the validity of intercourse's in Islam. I newly got married. Once we were trying penetration while standing. The attempt was briefly for 20 seconds. The standing position is a bit difficult position and I know that my full tip of penis never penetrated her vaginal opening. My wife says that it never penetrated her vagina. 

Now I am getting waswasa what if my tip of penis entered the vestibular area or got a cover from labia minora. What to do incase of doubt when the wife is sure that penetration never happened and I know I never penetrated her vaginal opening but not sure if the full tip maybe disappeared in to the vulva (Farje kharij). 

What to do in this case? What should be the case if my wife is certain and I am uncertain?

Making tayammum if it is not possible to make wudhu by oneself and there is nobody to assist

Q: I found the below statement about tayammum online, is this true? 

"If performing wudu causes extreme fatigue or is too difficult due to your condition (e.g., mobility issues or severe pain), you may: Seek assistance if someone can help. Use tayammum if assistance isn't available or feasible." Is this true? 

Washing a carpet purchased from a non-Muslim

Q: I recently purchased a room carpet from a non-Muslim which I intend using as a carpet to perform Salaah on. 

There are no apparent traces of najaasat on the carpet but there are a few stains which look like they may be from food or drink. 

The carpet is too thick and big to be soaked and squeezed. In order to ensure the carpet is paak, must it be washed once, then left to dry; then washed again and left to dry, and washed a third time and left to dry; in order for it to be paak? Or will one wash and soak be sufficient?