The answer can be both 'yes' and 'no'. The jury of scholars is still out, how can I student take it upon myself to answer the query. However, by logically analyzing the evidence presented by both schools, the answer tends towards "Yes. Uttara Kaanda is a later interpolation."
Based on the prime evidence in Chapter IV of Baala Kaanda and Chapter CXXVIII (...
Are there some foolproof methods of differentiating the originals from the interpolated texts in such cases? If yes, what are those?
There are some accepted methods explained further below but they are not perfect.
Are those methods mentioned in Hindu scriptures themselves?
For how the integrity of the Vedas is preserved, see this answer. I'm not aware ...
Not likely to be interpoloated.
There doesn't seem to be any strong enough reason for that.
"How can a serious philosophical treatise like Bhagavad-gītā contain verses like these that talk about astrology?"
It's not talking about Astrology, but liberation (Moksha). It's explained in description in How can we know that an Aatma got Moksha?. Below ...
One method had been used by Aacharyas is to prepare and check Anukramani.
For protecting the Vedas, and keeping the tradition of mantras well-organized, ancient Rishis has made sorted indices or index according to the topic/subject.
In these index Suktas, Padas, Seear of each and every mantra, Chhand (meter) of richa (hymns) and Devatas of Samhitas are ...
The critical edition of Vālmīki Rāmāyaṇa available at bombay.indology.info doesn't list the verse in question.
1004001a प्राप्तराज्यस्य रामस्य वाल्मीकिर्भगवानृषिः
1004001c चकार चरितं कृत्स्नं विचित्रपदमात्मवान्
1004001a prāptarājyasya rāmasya vālmīkir bhagavān r̥ṣiḥ
1004001c cakāra caritaṁ ...
I think not. The critical edition mentions 500 chapters in the text but most probably not the number of shlokas.
The table below shows the number of chapters and shlokas we have in
the Critical Edition. The Critical Edition has 606 chapters, 106 more
than 500 sargas mentioned in the text itself. And there are 18,670
shlokas. If one considers ...
Virata war is NOT an interpolation according to the BORI scholars. Beacause Critical Edition Prepared by Scholars at Bhandarkar Oriental Research Institute BORI > Devanagari (and other Indian scripts from each sarga page) > ४ विराटपर्वम् > ५६ contains the below verse:
ततो वैकर्तनं जित्वा पार्थो वैराटिमब्रवीत् |
Is the Uttara Kanda of the Srimad Valmiki Ramayana interpolated?
No, it's authentic and not an interpolation.
The last chapter called the Uttara Kanda is considered an interpolation, added in later time?
The only people who consider it an interpolation are Western Indologists; no ancient Vedantin or Vedic scholar has ever questioned the authenticity of ...