You can visit the official website for the HSK test dates. Choose your own language and there's usually a link on the homepage that leads to the test dates of the year.
The HSK certificate is valid indefinitely.
However, for academic purposes, it is valid for two years from the date the exam was taken. So if you're applying for a Chinese university, your HSK certificate will only be good for two years.
The test results dates are also on the official website on the same page as the exam dates. You can visit the official website here.
While the official website doesn't say anything about receiving the physical HSK certificate (you can check the scores at the published dates of the HSK Test results as I mentioned in the above question), simply contact your test center you took the test at if you have inquiries and they will help you.
If you hop on over to the website, you'll see that results are announced about a month after you take the test, so be patient for your certificate to arrive.
Hanban (public institution affiliated with the Chinese Ministry of Education) claims that the HSK levels have a one to one correspondence to the CEFR (Common European Framework of Reference for Languages) levels, HSK's Levels 1 – 6 to CEFR's A1 (Beginner) – C2 (Mastery).
In my opinion, levels C1 or C2 are really near-native, if not native levels of proficiency in a language. As an example, a person who has attained a C2 level of proficiency "Can understand with ease virtually everything heard or read. Can summarize information from different spoken and written sources, reconstructing arguments and accounts in a coherent presentation. Can express him/herself spontaneously, very fluently and precisely, differentiating finer shades of meaning even in more complex situations."