I wanted to know whether it is allowed and also plausible to submit two papers at the same conference? Does the acceptance or rejection of one affect the acceptance or rejection of the other paper?
There is nothing wrong or unusual in submitting two papers on a single conference. For specific detail you should refer to the conference author guide. In my experience, there exists an upper bound of papers (about 3-4), but I have never encountered a conference where only a single paper was permitted.
The acceptance or rejection is individual, every paper is peer-reviewed on its own account.
You should keep in mind that the conference will charge every paper separately. You should also watch the presentation schedule for any conflicts (though, they are very unlikely)
I wanted to know whether it is allowed and also plausible to submit two papers at the same conference?
Yes, it's generally allowed. (Unless the submission instructions explicitly forbid this.)
It's also plausible - it's even common. If your work is closely related to the scope of a particular conference, it's not uncommon for you to have multiple pieces of work to submit. (This is especially true if there are not many conferences in your subfield; you might choose to "save up" publications for a particular venue, rather than submit them somewhere else where they will be on the edge of the conference scope.)
Does the acceptance or rejection of one affect the acceptance or rejection of the other paper?
No, papers are generally reviewed independently and each submission of evaluated on its own merit.
Definitely check the conference website. For instance, one in my field (not CS admittedly) rejects automatically anything with the same first author.
My two little cents: It is of course generally allowed. I personally, did that a couple of times (2 or 3 papers). I have different experiences. There were conferences where both of the papers were accepted.
However, at one conference both of my papers were sent to one reviewer (though there were other reviewers). And that particular reviewer though that the underlying formulation of both of papers were same (!), which sounded as a serious accusation and the editor of the conference rejected one of the papers. I responded to the reviewers that the problems presented in two papers were completely different, though both of them definitely had some similar (15-20%) formulations. I am a PhD student working in a single funded research project; so there will always be some similarities in formulation among my publications.
There is another point to consider (which is my personal speculation) - when the conference editor/publication chair sees a number of paper from the same author, he/she might think, just might, you are using the conference as a dumping ground or just trying to save money (as usually papers after the first one gets some discounts) and reject the paper when the reviewers' give neutral comments. I may be completely wrong though.