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Seems old and should 5.4.45
Been running ElkArte fine on latest 5.6

1.0 is 5.2
1.1 is 5.3
2.0 will be 5.5

this site is on 5.4 if the headers are to be believed

your question is ambiguous

Mainly just this server for this site should be updated  for the security updates and performance.

Kind of thinking what we should do is up it to 7.0/7.1 and SSL

I would do 7.1 should be pretty easy at this point with MySQLI i have migrated most of my big projects to PHP7 just waiting for SMF....
SSL will be fine as long as their is an image proxy for any http:// images. Would fix the chrome issue with their new version coming out soon. I like to get SSL certs for 3 years so just have to remember one date to change it.  Also test your SSL on https://www.ssllabs.com/  to make sure you have  a secure setup.

I like that SSL test site, only because it gave me all A's 

There are a couple of image proxies for Elk available so we should be covered there.  

I'm not entirely sure we are all green with 7.1, but maybe we are and anyway direct testing would be the best way to know.
Anyway, fortunately for you, I'm not the sysadmin, so I'm not the one that should take the decision.