Congress has impeached nearly 20 individuals, and started proceedings on others. Most of those impeachment proceedings did not start with a full House vote to authorize a formal inquiry. So yes, you're cherry-picking.
Justice William Douglas
Judge Harry Claiborne
Judge Alcee Hastings
Judge Walter Nixon
And no, neither the Constitution nor US Code nor House Rules lay out any special procedures that require a formal vote by the entire House to start an inquiry.
And again:
Precedent is NOT BINDING on the House. It is the HOUSE RULES that are binding, and I literally pointed you right to those rules.
On a side note, I find the hypocrisy of conservatives rather thrilling, as they are perfectly happy to abandon precedent in genuinely binding situations whenever it suits them. The most obvious (but certainly not the only) example is
Roe v Wade, which conservatives would
love to directly overturn, even as they are insisting that the House follow a non-existent and non-binding precedent when it comes to Trump's impeachment.
The bottom line is:
• Trump very likely committed impeachable offenses by soliciting foreign governments to interfere with US elections, more than once
• Trump very likely is committing impeachable offenses by obstructing this process
• The current process in Congress is 100% legitimate, is within the guidelines set by the Constitution, is abiding by US law, and is following the rules of the House of Representatives
• Trump is almost certainly going to be impeached by the House
Also, see
https://docs.house.gov/meetings/JU/JU00/20190712/109768/HHRG-116-JU00-Wstate-GerhardtM-20190712.pdf
and
How Congress Can Access the Legal Powers of Impeachment Without a Formal Inquiry
Sorry not sorry, but you don't have a leg to stand on.