The oldest calendar I found in a panchangam published by a Sanskrit University for this year(2016) is as:
Vikram samvatsar: 2073
Kalergatabda means from beginning of Kali age and it gives present year as 5117.
Kalpadergatabda means from beginning of Kalpa and it gives present year as 1972949117. I don't know how it calculated such a precise value.
Shristyadergatabda means beginning of Shristi(Creation) in the Kalpa and it gives 1955885117 as present year. One may wonder why Shristyadergatabda isn't calculated from 1st day of Brahma, it is because creatures are in seed form in night of Brahma, so the continuation of calendar can't take place when calculated from 1st day of Brahma as worlds are destroyed in Kalpantak pralaya.
Here, the interesting thing to observe is Kalpadergatabda is 1972949117 and Shristyadergatabda is 1955885117.
If we subtract: 1972949117-1955885117=17064000
This implies creation occured about 17 million years after starting of this Kalpa. We have stories that Brahma created after some time when earth was created because earth was taken by Hiranyaksha in water at beginning. But I don't know how it calculated this time elapse as 17 million and 64 thousands years.
Hence Kalpadergatabda is the oldest Calendar.
For your another question use of calendar in our scripture. We don't find change in our calendar system because they were calculated by Trikaldarshi Sages and hence are eternal.
Years were calculated from both Lunar basis and Solar basis. This is evident from these verses of Valmiki Ramayana as you can see in my answer here.
As you can see there ninth day of bright fortnight is also there which is a lunar basis and Sun in Aries is also there which is a solar basis.
Also as you know Bhishma Pitamaha left his body in Makar Sankranti (when Sun is in Capricorn) which is solar basis and tithis are frequently used in Mahabharat which is Lunar basis. You can see my answer here for this.
Thus both solar and lunar sytem were used.
But solar year is 365 days and Lunar year is 29.5×12=354 days. Thus in 3 years Solar year becomes 3×365=1095 days and in 3 years Lunar year becomes 3×354=1062 days. The difference is 33 days. Thus there is 1 month more in Solar year in 3 years.
But for the synchronization of Luni-Solar calendar that specific month is termed as Adhikamasa and in this way Lunar and Solar calendar were continuously adjusted and it is done till now too.
Itihasas(scripture) doesn't directly speak about 7 days of week but as you can see in that verse of Valmiki Ramayana where all 7 planets are discussed. So days of week could easily be calculated. Days are just named on the basis of ruling planet at sunrise.
For eg. If the ruling planet during Sunrise is Moon than that day is Monday, if Saturn then that day is Saturday, if sun that day is Sunday, if Mars that day is Tuesday and so on. So the days of week are just representation of which planet ruled at sunrise at that day.
In this way our calendar systems were eternal.