I have presented a paper at a conference and received a certificate proving that I was a presenter. The conference does not have an English agenda, so it would not be easy for an application committee to find proof that I was the one who presented it online. I am now submitting the paper as one of my writing samples for a Ph.D. application. Should I attach the presenter certificate to the paper, in order to prove to the committee that I was really the one who presented it?
As per the answer to your previous question, you are not required to spontaneously supply proof for everything in your CV, and it would look extremely unusual to attempt to do so in this case.
The fact that you could be asked to substantiate anything written in your CV, and the consequences of subsequently being caught in a lie, are considered enough of a deterrent to prevent people from lying about their credentials. The standard practice in academia is not to include "proof" of everything on a CV unless explicitly asked for proof of some kind.
So in answer to your question of whether you should merge the "certificate of being a presenter" into the paper presented at the conference as part of your PhD application: No, you should not. You should not submit such a "certificate" at all unless you are explicitly asked for it, and I have never heard of anyone being asked for such a thing.
One thing to keep in mind is that certificates from a conference are easy to fake: anyone can make a plausible-looking certificate on their own computer, and the admissions committee will have no idea what a real certificate would look like. (And even if the admissions committee somehow knew what it should look like, an applicant could copy/modify someone else's certificate.) This makes them almost completely useless for verification. The certificates may satisfy bureaucratic requirements among those who use them, but in practice they won't actually prove anything.
I would recommend against including these certificates with your application. It looks suspicious to me, like you're presenting it as stronger evidence than it actually is. In particular, people might wonder whether you are trying to prevent a more detail investigation by preemptively offering a certificate.
However, this isn't a particularly important issue, since the admissions committee probably isn't worried about whether you actually presented the paper at this conference. A conference presentation is not meaningful or worthwhile for its own sake, regardless of quality. There are conference with low standards (where bad work is sometimes presented) or no standards at all (where anyone can present whatever they like). Instead of being worried about whether you presented the paper, the admissions committee will instead wonder whether presenting the paper means anything. That's much more subtle question, since the only way to convince them that the quality is high is if someone knows enough about the conference to judge its quality and is trusted by the committee. In practice, the way this typically works is that if the committee really wants more information, they find a member of the department who has a contact in the country in question and ask them for their opinion of the conference. (This can also lead to verifying attendance if necessary, since the contact will presumably have the appropriate language skills and can also get in touch with the organizing society.)