1) Among Dharmasmritis(Manusmriti, Naradasmriti , Parashara
Smriti,Yajnavalkya Smrti ... etc) , is there any verse or historical
evidence which suggests that manusmriti is more authoritative/followed
than others(Naradsmriti,Parashar Smriti,..) or whether all have equal
authority? What if two dharmasmritis verses clash with each other,
which one will prevail.
Medhātithi is his commentary on the Manusmriti says this:
Among Smṛtis Manu is most authoritative, as says Aṅgiras—.... as also the Veda.
Any Smṛti that goes against the ordinances of Manu is to be rejected—as declared by Bṛhaspati (see above). This is the view of the Kalpataru also
Also in the Veda:
We have the Veda itself testifying to the trustworthy character of at least one Smṛti-writer, Manu—‘Whatever Manu has said is wholesome.’
And the Parāśara Smriti:
Parāśara-Smṛti, 1.21.—‘During each Kalpa Manu declares the Dharmas.’
However, most texts state that all the Smriti texts including all the Dharma Shastras have equal authority, and the Manusmriti itself declares this:
The entire Veda is the root-source of Dharma; also the Conscientious
Recollection of righteous persons versed in the Veda, the Practice of
Good (and learned) Men, and their self-satisfaction.—(6)
The Veda should be known as the ‘revealed word,’ and the Dharmaśāstra
as the ‘recollections’; in all matters, these two do not deserve to be
criticised, as it is out of these that Dharma shone forth.—(10)
The Veda, the Smṛti, the Practice of cultured Men, and what is
agreeable to oneself—these directly constitute the fourfold means of
knowing Dharma.—(12)
Whenever there is a conflict between two Vedic texts, there is an option to follow either injunction.
Whenever there is conflict between Smriti and Vedas, Vedas take priority because they are more authoritative and because the Smriti texts are based on the Vedas.
Whenever there is a conflict between two Smriti texts, there is an option to follow either injunction, just like in the case of conflicting Vedic texts.
The Manusmriti itself says this:
Where there is conflict between two Vedic texts, both are held to be Dharma; both have been rightly pronounced by the wise to be Dharma.—(14)
Next,
2) 'DharmaSmritis' which are of later date, is there any evidence that Dharmasmritit's law has to be more authoritative than older 'Dharmasutra' (like Gautam dharmasutras)?
There is no Smriti or Shruti text that says that an older text is more authoritative than a newer one (and vice versa). The reasoning is because as long as Smriti agrees with Shruti, which is eternal, then it is authoritative.