Hurmat-e-musaaharah becoming established through touching a woman with lust

Q: I had read that hurmat-e-musaharah take place only if there was a lawful relationship. I just saw a post that if a man committed zina with a women he cannot marry his daugther. But if he wasn't married to that women and was mislead by shaitan.

Below is what I found.

On the other hand Imam Shaafi (rahmatullahi alaihi) is of the view that hurmat-e-musaharah is established only through lawful intercourse and not through unlawful sexual intercourse or touching.

Urine splashes on toilet seat

Q: I have had rectal problems for the past couple of years and I try to keep a slight gap at the back when I sit on the toilet. However, it felt like something fell on my back and I knew for sure it could not have been urine splashing on me. Later, I tried to check if urine splashes fell on me, but I couldn't tell. When I went the third time I saw one splash fall on the seat, so I was worried if this was happening all the time but I was unaware.

My questions are:

1. Do I have to have a shower and change anything that could have come in contact with me?

2. Are all of my prayers valid?

3. Have I made anything najis from touching that part of my body?

4. This is how most people use the toilet so should I tell my family members to be careful and sit all the way back.

Woman thinking of her father in-law

Q: If a woman thinks her husbands private part is her father in laws private parts or thinks they maybe similar to her father in laws private parts, and imagines her husband's private part and maybe also imagines the father in laws. Whilst having these thoughts (she hasnt actually seen them nor does she wish too) does thinking and imagining this affect the nikaah of the woman and her husband. She obviously knows her husband's private parts are his but she just got the thoughts explained above.

Calculating zakaat

Q: I wrote my gate exam. If I get qualified or get a rank then I will get a monthly stipend for my m.tech, around 12 500. Do I have to pay zakaat on that money?

If yes, then tell me the procedure. I mean is it compulsory on me to search for a needy person and give him or can I give it to anyone? Can it be added to an investment for the welfare of people/community by saving for public requirements in villages like for well, hospitals etc.?