The above questions may seem a bit strange but it is good to reflect over when you interact with social media.
If you have an active Facebook group then yes you should be pro-active and keep them post going in your on-line forum/group as such.
However it is important that you also keep your own web-site updated if you have a blog or news area. For the normal social media post the trick is to create the actual post on your web-site then highlight the hyperlink / URL (this would be the web address at the top i.e. http://www.yourwebsite.com/actualpost) copy this hyperlink / URL and post in into your Facebook post. If you have a business page at Facebook you will also be able to change the image to one of your choice. Maybe add some additional information and hit “post” and make sure that it is “public”. Now when the viewer sees your Facebook post and clicks it they will land on your actual web-site instead of your Facebook page.
The benefits for this is that the visitor might actually click on your other pages and see all your products and services. The more clicks your web-site pages will not only boost your direct business opportunities but also higher ranking with search engines and therefore more indirect business.
Another plus is that one you have done the post/article on your on site you do not have to do it over again in Facebook and / or other social media.