In a Republic running under the concept of Democracy what are normal citizens allowed to vote on and what can only be decided by officials

Here is something that really puzzles me. In a republic form of "democracy" who decides what legislations considered open for public votes as compared to those limited to voting within the government itself. In simple words what the public is or is not allowed to vote on or have a say. Apparently the population have little if any chance let alone getting a chance to cast ballets when it comes to passing of many driving related legislations in most juristications such as seatbelts that affect people's everyday lives as well as many other legislations such as whether styrofoam or plastic bags can be used in restaurants and grocery stores. However what is put into ballets usually include how money is spent in proposals to fund organizations such as transportation or school districts. Unfortunately most people either would not understand the complicity of the ballots or are not aware of what its intention so allowing them to vote on that issue is just not very practical its hard to understand them let alone to vote yes or now on those measures. Often the funding is not appropriately used after the ballot passes.   It seems like while governments in Republics often consider themselves for the people I often find them not representing the people as much of the population have no say in many things the politician decide for everyone to follow.  I always wonder why not let the population vote on issues that affect them the most and is easiest for them to understand. Otherwise what kind of democracy we have and what do are elected officials represent other than what he wants to represent.

Its important to know the subtle differences between republic and democracy. In a direct democracy all those with voting rights have absolute say over all things. In a republic however the minority's voice is heard as well as the rights of the minority is also to be respected.
In California surprisingly people are allowed to vote on Prop 8 which actually is a vote to change the constitution of California regarding marriage. Though California is officially a republic. A republic is a government that actually respect the rights of minorities as well. Republic essentially runs under the concept of liberty and justice for all therefore rights of the minority is actually a priority instead of mob rule in a democracy. Changing a state constitution certainly requires much more due process than just mob rule. Therefore a measure would require more hurdles than just 51% of "yes" votes. Another controversial  issue in California that people are allowed to vote on is the Three strikes law. Originally the intent is to lock away the most violent offenders kind of like lock them up and throw away the key mentality. However the three strikes law in California is wide open for abuse from overzealous judges as unlike other states with similar three strikes laws California allows a liberally defined any felony to count as a third strike instead of a violent felony. Abusive judges often illegally upgrade minor misdemeanors to count as felonies to get a repeat offender to be eligible for the third strike this is particularly true when these corrupt judges deal with African and Latin Americano groups. This has caused many disastrous consequences to the state as a whole such as prison overcrowding which forces real dangerous criminals back onto the streets, results in loads of state tax dollar funding be diverted to the prison system, results in third strikes criminals been even more dangerous as they have nothing else to lose and might do anything including killing and injuring innocents just to escape from being caught for a minor offense. Though many people might not understand the real issues of the three strikes law and the consequences they face as a result and might vote no on it being "soft on crime."

There are many unanswered questions in a about whether the officials actually represent the people who elected them or they seem to represent themselves or the organizations who are friends with them but enemies with much of the public. Why we have no say or vote on most traffic related issues. Why are we allowed to vote on marriage issues but not on what firearm or fireworks we are allowed to own or to use? Why are we allowed to vote on certain measures regarding schools but not the school calendar or curriculum in our neighborhood schools? Therefore I always wonder who or what determines whether a legislation change is open to voting by the general public as opposed to only in the Assembly or the Senate or in the Supreme Court of California?