Meaning of the hadith “War is deception”

Q: Abu Hurairah and Jabir (may Allah be pleased with them) reported that the Prophet (ﷺ) said, “War is deception.” [Al-Bukhari and Muslim] 

Is it permissible to deliberately spread a false rumour accusing the wife of a prominent political enemy of the Muslims of adultery, with the intention of discrediting him, causing turmoil and distress in his personal life, and thereby hoping to gain a strategic advantage for the Muslims?

Calculating the value of gold for previous years' unpaid zakaat

Q: I wanted to ask some things related to the payment of zakaat. They are as follows: 

I was unaware that I had enough gold previously and now I have to pay zakaat for the last 2.5 years. So will the zakaat of each year be calculated according to the gold value in that year, or according to the current year's gold value? 

If I won't pay it all at once, and do it in installments will I be sinful in delaying it further?

Sleeping after fajr

Q: I wanted to know sometimes I get up and perform tahajjud 1 hour before the time of Fajr but after performing my Fajr I doss of many times and put my alarm for ishraaq salaah to get up again. Is it permissible for me to do that ?