When does Tahajjud time end?

Q: I have two questions which I kindly request you to answer me.

1. I have doubt regarding tahajjud Salaah. I want to know when it exactly ends. Say the fajr Salaah starts at 5.23 am in where I live , now. Till wheat time then can we pray tahajjud Salaah? I want to know the timing so I can rectify if I make any mistakes.

2. Can we recite salawatun naariya with a particular niyat to be fulfilled? Where I live people recite it 4444 times with a particular niyat he or she has. Is it permissible?

Hurmat-e-musaaharah

Q: I wanted to clarify something. I know that by touching a female with lust, the ruling of musahara applies. This is also the case if touching through a barrier but body heat can be felt. If a person is in close proximity to someone, without touching them, they may still feel their body heat that is being released, would this still necessitate musahara? If the man felt lust at the time of feeling this heat? That is, no physical contact occurred, but he felt the heat of the person with lust. Also, is the restriction with any lust, or does erection have to occur in the male who was touching?

Performing qasar Salaah while travelling to one's destination

Q:

1. If someone intends traveling to a place more than 55 miles (i.e. 88 km) from his hometown but intends staying at his destination for more than 15 days, will he do qasr while traveling to that place?

2. If a person intends going to a place more than 55 miles (i.e. 88 km) from his hometown. After reaching he intends to stay for 15 days. Later on he changes his mind and intends to stay for 2 days. Will he be musafir or muqeem?

Inheritance

Q: My sister died in 2004 and she had £365000 in her account cash and interest accumulated to £40000 making a grand total of £405,000.00. This had been divided amongst 17 members of family without paying Zakaat since 2004. She died in 2006 what is your opinion?

Working for a company that rents out ticketing software

Q: I am working as a business development executive for a company which develops software for theatres, food court and parking. However, the software has no concern with movie, it is being used for ticketing purposes. Moreover, my company supplys computers to theatres on rental basis for ticketing purposes. Kindly, guide me whether my job is valid as per our shariat.