Here’s my take on your five questions –
1. is the House legally required to find?
Prior to an actual vote to impeach, the House could (but, won’t) scuttle this whole process, by simply announcing that impeachment is off the table.
2. is the House restricted to only two decisions - Impeach or Not Impeach? - or can they find differently?
If impeachment is brought to a vote (as it will be), there are only two possible outcomes: (i) The vote to impeach passes, in which case the President is impeached, or (ii) the vote to impeach fails, in which case the Democrats will have a lot of egg to wipe off their faces, and Trump will have Tweet-material to last through his second term, and beyond.
If the House scuttles the impeachment effort prior to actually taking a vote on the question, there are other ways they can try to embarrass the President: They could, for example, pass a resolution of censure, which is a purely symbolic gesture – about as meaningful as the U.S. House of Representatives censuring the British Prime Minister.
3. is the House legally obliged to pass an Impeach decision to the Senate?
Yes. If the House votes to impeach, then the President will be (essentially) indicted or charged. In this case, the U.S. Constitution provides that the Senate will try the President on the Articles (specific charges) sent up by the House of Representatives.
Note: It’s theoretically possible for only one of the two Articles of Impeachment currently under consideration to be approved. That is, the President could be impeached on Article I, but not impeached on Article II. In that case, the Article (singular) of Impeachment sent up to the Senate would be tried by the Senate.
4. is the Senate legally obliged to hear the case?
The Constitution does not say that the Senate may (or may not) refuse to hear the case. But, it’s generally accepted that the Senate has the obligation to deal with it in some manner.
Here is the exact language in Article I, Section 3 of the Constitution:
The Senate shall have the sole Power to try all Impeachments. When sitting for that Purpose, they shall be on Oath or Affirmation. When the President of the United States is tried, the Chief Justice shall preside: And no Person shall be convicted without the Concurrence of two thirds of the Members present.
Judgment in Cases of Impeachment shall not extend further than to removal from Office, and disqualification to hold and enjoy any Office of honor, Trust or Profit under the United States: but the Party convicted shall nevertheless be liable and subject to Indictment, Trial, Judgment and Punishment, according to Law.
(1) There has been a suggestion that the Senate (i) receive the Articles of Impeachment (assuming the House approves them and sends them on), (ii) read the Articles into the record, acknowledging that they have been received, and (iii) then (without debate) immediately vote to convict or acquit based on those Articles – a vote that would surely result in acquittal by the Republican majority.
Whether this would spark a so-called constitutional crisis, I can’t say. (But, it would certainly cause Senator Schumer’s head to explode.) If a constitutional crisis ensued, it would obviously be over the question of whether “the sole power to try all Impeachments”, as worded in the Constitution, implies the obligation to try all Impeachments.
(2) Article I establishes the legislative branch of the U.S. government – the Congress – consisting of the House and the Senate. Even before establishing the President as chief executive (in Article II), and the Supreme Court and the rest of the federal judiciary (in Article III), Section 3 of Article I establishes the procedure for removing the (yet-to-be- defined) President, in a trial presided over by the (yet-to-be-defined) Chief Justice of the Supreme Court.
(3) Note the German-style capitalization of nouns, as rendered by the authors of the Constitution. And note also the peculiar placement of colons in two places in the portion quoted above (after the phrase, “…the Chief Justice shall preside:” and after the phrase “…or Profit under the United States:”
5. is the Senate legally obliged to find only either Guilty and Not Guilty? - or is there an alternative verdict?
It’s a binary choice – either Convicted or Not Convicted – on each Article of Impeachment.
Presumably, if two Articles are sent to the Senate, they will be voted upon individually, and theoretically the President could be convicted on one, but not the other.
But, this is strictly a political process, wrapped in the trappings of a legal process. As a (partisan) political process, the chance of a conviction on any Article of Impeachment by the Republican-controlled Senate is nil.