A quick answer: your analogy isn't quite right. The Constitution gives the House "the sole power of impeachment." So unlike you, their work is never "going to court." No judge is ever going to look at the evidence they used and say, "You only used notes, not a final report. That isn't good enough, or admissible."
A longer answer: impeachment is not a legal process. It is a political process. The only binding requirements are those found in the Constitution. These cover who can be impeached and tried, for what, how punished and by whom.
All other matters of procedure are decided by each house. There are several sets of rules and precedents that cover impeachment. But if the House or Senate decides to ignore these rules and make up new rules, they can. After all, Article I of the Constitution gives each house "sole power" over impeachment and trial. It also gives each house the power to "determine the Rules of its Proceedings."
You might ask, why, if impeachment is a political process, do so many people talk about it as if it was a legal process? The answer is simple: Both sides are busy trying to put their spin on what is going on in the House. If either side believes they will get more support by talking about impeachment in legal terms, that is how they will talk about it. But this spin should not hide the reality: impeachment is political.
That impeachment is political does not mean that it should not be guided by the same values that guide legal processes. Of course, the hearings should be fair, the President should get due process, and so on. But because they are political, no court is going to step in and assure that they are fair.
The only guarantee that the President will get a fair hearing and due process is also political. If enough Americans think he did not get treated fairly, or was denied due process, or what impeached unfairly, they can vote the Democrats out of office.
Politics is the key to understanding much of what has gone on so far in the impeachment process. For instance, for a long time, Speaker Pelosi refused to hold a vote on whether to formally start impeachment proceedings. She offered a variety of explanations for this, but the truth was that she did not want to force Democrats from close districts to have to openly vote against the President. Similarly, Republicans, who wanted to force Democrats from close districts to vote against the President, argued that it was unfair, illegal or unconstitutional to have any hearings on impeachment without such a vote. Since there are more Democrats than Republicans in the House, Democrats got to decide when that vote was held.
Of course, if the House does impeach, and the Senate has to try the President, since Republicans control the Senate, they will control the rules, etc.