Hashtagging is not a Facebook thing, it is something used in groups for the administrators to be able to control activity.
For this reason, is it important to know and respect the rules of the group? They will have certain days for certain things and if you do not respect the rules you will be kicked out. The rules will normally be on the right-hand side of the page or have a look at the announcement to know what you need to know, this is important, it is proper group etiquette.
#thread is like for like.
When they have a #thread day you can go into the comments and post your URL. Always have your URL handy to be able to copy and paste it. You don’t necessarily have to use the #thread command. You can then go through them and like the pages that are interesting to you; they, in turn, will then hopefully return the favour. What I like to do is put a little elevator pitch sentence with my URL so that they know what I am about. A lot of people don’t do that but I encourage it.
#event is very similar.
You are allowed to share your event. If you are sharing your event in the post you do not need to use #event. If you are posting it onto the page then you do. Again, be aware of the rules, know when you can and cannot share events.