We are happy for your interest to know about sage Viswamithra. There were no many viswamitras, like other sages. Only one was there, who was highly praised by Sage Valmiki.
When you talk about the age, in those days they used to live long, like thousands of years. It was not a big issue in those days at all. Sumanthra the minister of Dasaraddha, Ravana, Vasishta etc., were living even in Krutha Yuga.
So also Viswamithra. Now a days, we people started comparing with our own knowledge and age and experience, which is wrong.
Another Lo:ka created for Trisanku by the same Viswamithra, who was having enimity earlier with Sage Vasishta. Menaka met with the same Sage, yes!
To his own credit he made penance for thousands of years on each corner of this country. He met with different issues on each of these corners. But he was the same Sage.
Rama belongs to Surya Vamsa. After Rama, approximately 32 generations were continuing. Then there may be some gap. During Rushabha Deva again the Chandra Vamsa started in Ayodhya. This might have started after a few lakhs of years,
when dwapara yuga was started.
Some people say that yugas go in some thousands. Even that is wrong. They go in 4:3:2:1 ratio, which altogether come to 43,20,000 years. The size of human beings also was not as we see them today. Recently, some skeleton found in North
Indian Desert was so amazingly huge, may be between 30 to 50 feet height. There was some record also found along with it, which was not totally revealed by the Govt. but says that they were interacting with brahma and Siva etc. we try to
put that available information for you soon.
So people living for thousands of years was not a great thing in those days. Finally, it was the same sage Viswamithra, who was mentioned in all the episodes you have memtioned and he lived for many a year, before and after Rama.
He did not appear in Ramayana after Rama’s marriage, but he was there. We are not sure whether Viswamithra’s mention was there anywhere in Lord Venkateswara’s History?