Based on my experience teaching and living in East Asia I would say that online TEFL certifications are usually accepted when required by the school. The requirements to teach abroad depend on the school and sometimes country. Rarely are TEFL certifications required for any visa application, however certain schools may prefer teachers to have one.
However, just like your degree (or any onsite course) they don't guarantee anything everywhere.
How to check if a TEFL/TESOL certificate is valid?
If you are an employer and you want to check if the certificate is real then usually you will see a unique TEFL certification number on the bottom of the certificate. You can then contact the company that issued the certificate and have them double check if the number matches.
ESLinsider's TEKA course includes this.
If you can't find out any information about the company or even a website then perhaps it is a fake certificate.
How do I verify my TEFL/TESOL certificate?
You can notorize your certificate by making a copy of it and then by visiting your local town's notary public or if abroad you can go to your embassy. They will then stamp and sign it to verify it in front of you that it is indeed real. This can also be done with degrees and other certificates.
An apostille is sometimes required for diplomas and certificates and this is one more step. You can read more on apostilling your paperwork for Korea (it is often the same process for other countries when required).
Do TEFL certificates expire?
No, not really. Although there are some things that you should keep in mind. It's often better to take a course close to the time that you will be teaching. Typically it is good to take a course before you start, but a good course can be especially beneficial to take after you start as you will have more context for teaching.
When you take a course before you start you don't have any context for teaching. It's an abstract thing and this can cause the information to go in one ear and out the other. Also if the course is low quality and online without any visuals of teaching in action you are unlikely to absorb what you are reading.
See Are online TEFL courses any good? for more.