Can we use the word 'eldest' for a high status person? If we want to say that A has higher status compared with another man, can we say, "A has always been eldest of all (exalted)"? What about the word 'senior' in this case? And, does the word 'senior' only denote experience and professional career?
Here are two senses of senior by Merriam-Webster:
1 : a person older than another • five years my senior
2 a: a person with higher standing or rank
In the second sense of senior, you could say that the most senior person has the greatest status. However, if using the first sense of the word, it just means that they are the oldest.
Here is one sense of seniority by Merriam-Webster:
2 : a privileged status attained by length of continuous service (as in a company)
And here is Merriam-Webster's definition of eldest:
: of the greatest age or seniority : OLDEST • my eldest daughter
Although typically it's used to refer to age more than seniority, even if you understand eldest to refer to somebody who has the most seniority, that doesn't necessarily mean that they have the highest status.
A mid-level employee could have been at a company for the longest amount of time, while a CEO could have just been hired. In this case, the employee with the least seniority is the person with the most authority and status.
Merriam-Webster also provides a sense of elder, which can be used in relation to leadership::
3 : one having authority by virtue of age and experience • the village elders
However, despite the way you would think English works, in this particular case, eldest does not mean the elder with the most authority.
Even the phrase the eldest elder (something that doesn't sound natural) would normally be taken to mean the oldest elder, which is not the same thing that you have in mind.
So, while some of these words have such associations in some cases, they don't actually mean what you're thinking of outside of some specific contexts. (In some religious orders, for example, the Abbot of a temple—the highest ranking member—is the most senior monk.)