No, the terms are not all contemporary. Afghanistan is recorded in the 13th century; some of the others appear to date to the 20th century. Pakistan is 1933, the others probably date from either the Soviet federation or independence in 1991
Also note hat tip to @jamesqf that Balochistan is a -stan predating Pakistan, therefore not all the -stans appeared simultaneously. I can't find a clear date for the first use of the name Balochistan, but it is earlier than Pakistan.
Below I've provided superficial answers to what seemed to be the core of the original question. I'm not clear on the scope of the ancillary questions, but the sources provided should provide a starting point for further research.
Note that in several cases it isn't clear whether the term refers to a state (OP specifies a "sovereign state") vs a subordinate political unit or a culture area
The earliest mention of the term "Afghanistan" appears in the 13th century in Tarikh nama-i-Herat of Sayf ibn Muhammad ibn Yaqub al-Herawi, mentioning it as a country between Khorasan and Hind, paying tributes to the country of Shamsuddin. Wikipedia:Afghanistan
See The So-Called Virgin Lands of Kazakhstan 1962 hat tip to @jan
Kazakhstan was the last of the Soviet republics to declare independence during the dissolution of the Soviet Union in 1991. Wikipedia:Kazhakstan A more complete treatment can be found in Wikipedia:KazakhSovietSocialistRepublic
hat tip to @default-locale with minor edits "Kazakhstan" was supposedly mentioned in XVI century work by Zainuddin Mahmood Wasifi (source in Russian, (no English translation available)). Both "Kazakhstan" and "Uzbekistan" were widely used in the early XX century. For example, the newspaper was renamed to "Socialistic Qazaqstan" in 1932 and "Uzbekistan" was mentioned in 1928 magazine.
The name of the country was coined in 1933 by Choudhry Rahmat Ali, a Pakistan Movement activist, who published it in a pamphlet Now or Never, using it as an acronym ("thirty million Muslim brethren who live in PAKISTAN"), and referring to the names of the five northern regions of the British Raj: Punjab, Afghania, Kashmir, Sindh, and Baluchistan. Wikipedia:Pakistan
Tajikistan has existed as a state only since the Soviet Union decreed its existence in 1924.StateUniversity.com
See Soviet Turkmenistan, a work from 1956 hat tip @jan
The name Turkmenistan is derived from Persian, meaning "land of the Turkmen". Before 1991, it was a constituent republic of the Soviet Union, called the Turkmen Soviet Socialist Republic. mcgill.ca
During the Soviet era Uzbekistan was the equivalent of an American state known as the Uzbek Soviet Republic. It became Uzbekistan after independence in 1991. FactsAndDetails