Let me start off by saying that I don't think is a good question for Hinduism Meta.SE. Much of this is better handled through the main site, through methods like voting, commenting, chatrooms, etc. But let me address your points one by one:
First of all there are many quotations from Vedas by ancient scholars which aren't found in todays versions/recensions. This doesn't prove that Vedas are heavily interpolated and similar for other texts too. There are also recensions of Puranas and when something isn't found in Purana it doesn't make it heavily interpolated.
This is a substantive criticism of my answer, justified or unjustified, and it has no place in Meta. If you think my answer is incorrect, you are free to downvote it. If you would like to point out something that you think is incorrect in my answer, you can post a comment on it. And if you would like to discuss something I said in my answe, we can do so in one of the chatrooms. But regardless this is not at all an issue of whether my answer breaks the rules of the site or not, which is what would be relevant for Meta.
Oh really! Which are these so called ancient works and which are the quotations that are not found. At least I know that one ancient work is Agama Pramanya of Yamunacharya where two quotes from Linga Purana are quoted and both are found in Linga Purana as I have answered.
If you would like to know which ancient works these are, you can look in the book I cited. But again, this is a criticism of the substantive accuracy of my answer, not about its conformity to rules.
Who are these some people? Are they propagators of Hinduism? Are they ancient Acharyas? Are they some western scholarly works? He gave a book of some author. On reading surfacely this book contains things like: "This Kurma Purana passage contains things of Saivite origin and it also contains somewhat principles of Pashupata so it is of early origin and can't be latter than 700 AD." Oh so, this is the scholarly level of book. Interesting!
Now I am a Hindu, and as such I believe that the Kurma Purana was composed by Krishna Dvaipayana Vedavyasa over 5000 years ago, not any time in the vicinity of 700 AD. But we must keep in mind that this is not a Hindu website, but a website about Hinduism. And as such it is fine to quote the viewpointsof scholarly works about Hinduism, even ones written by Western Indologists.
Narada Purana contains Anukramani of every Purana and in the description of Linga Purana, it perfectly matches with the present Linga Purana Version. So, how is it that it is a complete interpolation? Obviously you may claim Narada Purana is also intetpolation. Nice!
This is again a substantive argument against my the correctness of my answer, and again it is irrelevant to Meta.
Note that the references of Lingodbhavam are found in plenty of poems of Sambandar (western dating 7th CE) and in also Tirumantiram(5th CE western dating), even the Skambha Sukta contains the reference that Prajapati taking a form of bird and going up towards Skambha. So, I'm not sure what is suggesting him to take it as interpolation.
Then you are free to raise that issue with me on the main site.
Oh so it's based on conclusion of scholars based on things like style of languages. Ok I see. If I see based on style of languages there are plenty of scholarly works which say that except Brihadaranyaka and Chandogya nearly all other Upanishads are post Buddhist, so whenever I quote from other Upanishads am I allowed to write:
"One note of caution: These Upanishads like Mundaka and Prashna which I have quoted above are considered by many scholars to be post Buddhist so take it with a grain of salt."
Yes, you are allowed to say that. Now as a Hindu, I think you would be wrong to say that, but again this is not a Hindu website, but a website about Hinduism. We welcome people from all points of view here, as long as they follow the rules.
Or should I write: ... Or should I write: ... Or should I write: ... Or should I write:
Yes, are you allowed to say all of those things, whether I agree with those things or not. If you are an atheist and you are answering a question on what the earliest scriptural reference to the caste system is, you can post a quote from the Purusha Sukta and and say that it's considered an interpolation by Western Indologists. That would be perfectly relevant to answering the question, and while Indisagree with the notion that the Purusha Sukta is an interpolation, it would not be against the rules of the site to post.
So, I want to know on what basis is one claiming that one Purana is a complete interpolation, on what basis is one claiming that Ganesha popularity latter increased only?
Again, I'm perfectly happy to answer that, but Meta is the wrong place to do so.
Ganesha is son of Parameswara and Shakti. He is in exalted position always.
You don't need to tell me that. Have you seen my room? But again, this is irrelevant to Meta.
So, on what basis is he making the claim. If his basis is some so called scholarly works, why should not I also quote some other scholarly works which say like Bhagavata Purana is post Ramanuja work, Vishnu purana got it's complete form during about 7th CE, Vishnu is just a helper of Indra in RigVeda and latter texts like Puranas were made just to glorify him etc.... etc...
Yes, you are free to quote such scholarly works. And if people disagree with you, it should be handled through voting, commenting, etc, not through moderation.
So, first of all I ask the community whether these types of activites are allowed or not?
Yes, discussing interpolations in Hindu scripture is completely allowed on this site. And moreover, when I discuss interpolations, it is completely relevant to the answer at hand. If I post a story based on some Purana, and I think there's good evidence that the story is an interpolation in that Purana, then it serves the accuracy of the answer to mention that fact.
By saying that Linga Purana is completely interpolated, he is insulting Purana itself, he is insulting Sãdhakas who are doing various Sadhanas like Vajreshwari Vidya, Mrityunjaya sadhana based on Linga Purana; he is insulting devotees who are worshipping Parameswara with hymns of Linga Purana.
I am not insulting anyone. To make a statement of fact, especially when backed up by sources as I did in the Linga Purana case, is not an insult. Now if you disagree with the correctness of the statement, again that is to be handled by voting, commenting, etc. But for the record, I do not condemn the Sadhana of anyone. It could be that that Sadhana is perfectly authentic, but it may not originally be from the Linga Purana, but may instead be from some other scripture.
So, I suggest him to keep his scholarly works in his pocket or he can express it in sites like Mythology SE or History SE which maybe suitable place to do so.
No, this is just as suitable place to post such things as Mythology.SE and History.SE. Again, this is not a Hindu website, but a website about Hinduism.
We can also come of with tons of scholarly works and quote in last section of answer and in that case you might find it difficult.
You are free to do so, if you think the statements you are making and the works you are citing are correct. But if you want to do it as some kind of retaliation, I would advise against it.