Pre-revolutionary English judicial precedents unless overturned by
American acts of Congress have a forceful effect in American law,
In many circumstances, it does. Sometimes this is done to inform judges regarding the original intent of constitutional provisions in that era by providing non-binding but persuasive context for the language in the constitution.
Sometimes, it is part of a common law legal tradition of precedents that was not displaced by the American Revolution.
Also, state and local legislation can and often does displace pre-Revolutionary era English common law precedent. Indeed, this is much more common than Congressionally enacted laws doing so, because most subjects for which there is English common law precedent are matters of state law and not matters of federal law.
Otherwise how do you end up with the scotus citing the right of
eminent domain etc?
Eminent domain is expressly provided for in the 5th Amendment to the United States Constitution. Precedents in place in 1791, when it was enacted, merely provide context for what was meant when the 5th Amendment was adopted.
What is the basis for this continuation of English common law and how
did it come to be?
English common law was the law in force at the time of the American Revolution and was not displaced. The status quo was merely continued. And, in the 18th century, the prevailing legal theory saw common law as largely a form of natural law that was "discovered" in much the way that a scientific law might be, rather than being a policy choice made by a judge. This legal theory of the common law, however is no longer current.
These days, many states have statutes that expressly make the common law of England in the year 1776 (or some other year established by law) the default rule of law in circumstances where there is no other legal guidance.
For example, Section 2-4-211 of the Colorado Revised Statutes states that:
The common law of England so far as the same is applicable and of a
general nature, and all acts and statutes of the British parliament,
made in aid of or to supply the defects of the common law prior to the
fourth year of James the First [i.e. 1607 CE], excepting the second section of the
sixth chapter of forty-third Elizabeth, the eighth chapter of
thirteenth Elizabeth, and the ninth chapter of thirty-seventh Henry
the Eighth, and which are of a general nature, and not local to that
kingdom, shall be the rule of decision, and shall be considered as of
full force until repealed by legislative authority.
In practice, however, as U.S. common law courts have developed a large body of common law precedents, resort to English common law cases as a binding rule of decision is almost non-existent. I doubt that even one in a hundred appellate court decisions in the U.S. refer to it as binding law, perhaps one in a thousand cases is closer to the mark.
Instead, the most common modern practice, when a particular state encounters a question upon which the state's appellate law has no relevant precedents on a question reserved for the common law is to look to the most recent "Restatement" of the law, a series of non-binding code-like summaries of various common law legal subjects that is a mishmash of majority rules and "better rules" when there is more than one rule used in state courts, prepared by eminent legal scholars called "reporters" in a process supervised by the American Bar Association, or to look at the precedents adopted by courts making common law rules of decisions in other states presented with the same issue.
What parts of the English jurisprudential and legislative mechanisms
were done away with and which were kept? Why?
While Congress and state legislatures were informed by English legislative mechanisms in devising their own laws, English legislative mechanisms were immediately dispensed with at the time of the American Revolution in 1776.
English jurisprudence continued in continuity in substantive common law everywhere but Louisiana (which had a French civil law tradition that persists with modification to this day) and Puerto Rico (which has a Spanish civil law tradition that continues to this day with modification), since it was the status quo. But it developed largely independently of English law since then, as American precedents were developed. As a result, there are now very few areas (all obscure) where American precedents are not on point to provide a rule of decision, making resort to English jurisprudence unnecessary.
Still, when a concept, doctrine, or legal term originates in English common law, it isn't unheard of for American courts to elucidate the English origins of the idea as part of the process of explaining the modern meaning of the legal idea or term in question, as much for "color commentary" as for a source of binding law.
In some areas, like property law, parts of the United States that were formerly part of Mexico likewise continue Mexican private law traditions and jurisprudence. There is some residual Dutch jurisprudence in New York State that had a Dutch colonial period. And, as mentioned before there is a primary French legal foundation of private law in Louisiana and a primarily Spanish legal foundation of private law in Puerto Rico.