Was it a representative republic?
It did have representation of some sort, the parliament was a remarkably democratic body
for the times. It had a monarch, so, by definition, it was not a republic.
Did it have a Constitution and a Bill of Rights??
It had a series of documents and unwritten precedents often referred to as the "British constitution", like the Magna Carta and the Monarch appointing a cabinet to "advise" them in the exercise of their executive powers (in practice, the cabinet ran everything, and the monarch appointed who parliament told them to appoint). The American Bill of Rights was, in fact, inspired by
the English Bill of Rights of 1689.
Did it have 3 equal branches, an executive, a legislative and a judicial?
The American model presidential system was in fact based on the British system, where the King was the executive, the bicameral parliament was the legislature, and the judiciary had a long established history of independence. That's why the people who proposed it were often attacked as anglophiles, the true radical republicans wanted a unitary council of some sort, not any of this monarchy tainted three branches bicameral nonsense. Of course, with the increasing legitimacy of democratic ideas and the wane of aristocratic ones in Britain, the monarch increasingly gave up all executive powers to the prime minister and largely waived his right to dissolve parliament or appoint the a PM of their choice, and the house of lords had it's powers reduced to the point where it's barely relevant today, so, ironically, the current British system has largely come to resemble the system proposed by the radical republicans than the American system does today. Of course, the judiciary in Britain does still retain independence of some sort under precedent, but they are clearly subservient to the bicameral-in-name-only parliament under the doctrine of parliamentary sovereignty.
Were citizens able to vote in democratic elections for their representatives on a local, state and federal level???
Citizens residing in Great Britain, pursuant to certain qualifications (which were indeed high in those days, but the requirements were initially high in the American republic as well), were allowed to vote for their member of the Commons. A citizen residing in the colonies wasn't given such a right. But neither is an American citizen residing in Puerto Rico. There were local councils, but there wasn't any middle level of federation.
Was it possible for any citizen to become a prominent member of local, state or federal government????
You could become Prime Minister if elected and appointed by parliament. This was obviously heavily tilted in favor of the wealthy, but that is even true today in modern America, and was especially true in the early days of the republic. Of course, back in those days as well the democratic parts of government had to share power with an unelected house of lords. But in the early days of the republic the senate wasn't elected either. And the senate became elected around the time the House of Lords began losing it's relevancy, the early 20th century.