Regarding preservatives in food
Two factors may be at play. (1) While bacteria and molds do indeed grow on sugar, a very high concentration of sugar inhibits growth. So fruit preserves, syrup, honey, molasses etc. do not need to be refrigerated and generally do not require other preservatives to be added. Soft drinks contain less sugar and are more susceptible to spoilage, hence the use of preservatives. I would definitely refrigerate a soft drink after opening it, if not consumed immediately. Acidity also helps inhibit growth (e.g. sweet pickles). 

(2) Another factor is that bacteria and molds require water for growth, so foods such as dried fruits, that contain a moderate level of sugar but only a small amount of water, may have a long shelf life.