a) If I click on Quattro Pro's icon, it starts up normally in a full-screen DOS session. But trying to open the "Icon" page in its Properties still freezes the system and it's CAD Time.
While there may be an issue with QP's icon, I'd suggest trying something else first.
In 'c:\os2\install' you'll find a file named 'database.txt'. Rename it. This is a listing of known DOS & Win3 apps along with the specialized DOS/WinOS2 session settings for each. When you create a new program object for one of these apps, the system automatically imports the associated settings (or at least, it used to). In the past this was known to cause problems sometimes, so it's best to eliminate it as a suspect (you can always open it in Text Editor and manually apply these settings - both WS and QP are listed).
Trash Can's Properties do not seem to offer any way to change the icon. Is this a Sinister Indicator?
Unlike other folders, Trash Can's icons show Empty/Full rather than Closed/Open. I guess the original author didn't want you screwing up his handiwork.
d) How do I configure the Drives to open in icon mode by clicking on them, not on the "Open As..." menu option? Believe me, I have searched for a setting that stays put.
In addition to the Menu page in its notebook (which has been there since 1992), there's also what may be XWP's single-best enhancement: Select 'Open as', then shift-click on the view you want as the default. Drive objects can be "difficult" and may require you to do this twice.
And Drive names also seem immune to the normal name-changing procedures (such as that page in Properties).
Drive objects are recreated at each restart and assigned a name formulaically. You can select a different "formula" by opening the Drives' notebook to the misnamed 'Drive icons' page and selecting one of the alternatives. All changes are live, so have the Drives folder open to see the effects.