Why did he think that only with the DEATH STAR around was it safe for him to dissolve it? And during that time was it just symbolic body or did it have some serious influence and impact, what with people like Leia able to be elected and vocal/active?
The senate has been virtually powerless ever since it granted emergency powers to Palpatine in Attack of the Clones. The little power it pretends to have is clogged with bureocracy and procedure. However, only with the Death Star could Palpatine finally end the charade and openly dissolve the senate without any fear of repercussion across the galaxy with a widespread support for the Rebel Alliance. This is all established in the dialogue between Commander Tagge and Tarkin.
The Imperial Senate was responsible for much of the basic functioning of government. Presumably the Emperor had veto power over any laws passed and the ability to write edicts that were de facto laws without Senate oversight, but all the nuts and bolts didn't come directly from his office. By the time of the Death Star completion the Moff system is sufficiently established that they can replicate the day-to-day governance, and the illusion of democracy can be fully wiped away. "How will the Emperor maintain control without the bureaucracy?" - this dialogue makes clear that the Senate IS doing some actual governing, but has limited power to make real change.
1. The illusion of some choice in Imperial matters. 2. Bureaucracy. Just Palpatine and his executive staff aren't enough for those 19 years.
You know, until seeing this just now, I hadn't fully appreciated the (almost certainly deliberate) fact that that's exactly the persuasion tactic Palpatine uses to get Valorum voted out in order to take his place. At the risk of invoking real life politics (let's not go there lol), it's frighteningly fascinating how Lucas wrote it so that he began as a politician who points out an issue and promises to fix it, all the while his ulterior motive being to facilitate it even further for his own benefit