How can you not allow digital signature to be forged? I know digital signatures can be forged by creating and using someone's name. Please help.

Let's talk about digital signatures and forging, this is very important. All your users will need to understand this, otherwise they will be completely vulnerable to forging.

Digital signatures are based on a certificate, which has public and private parts.

The private part must be kept absolutely safe and private. If someone gets a copy they can sign anything as that person.
The public part is meant for sharing. And the sharing is crucial.

Let's imagine a paper based system for a moment. If a letter arrives asking for a million dollar transfer, you would want to check it. How would you check it? Perhaps the signature is in a filing cabinet. You assume the file has been kept safe - that people can't wander in and change the file. Then at least you can trust the paper signature to check it.

It's the same thing with digital certificates. The public certificate is shared FIRST. This process, done once, has to be trusted. If a certificate arrives claiming to be from someone, you must check, otherwise the certificate might be a fake. Human has to talk to human here.

Once you have the public certificate, you can check whether any future PDF used that exact certificate. NEVER look what it says on the page, that could be a fake.

Public certificate stores are an alternative to sharing public certificates. It basically means all the certificates are held by someone you trust who has already made all the checks.

Not possible.

You can only accept trusted certificates.