Shimano Di2 plays nanny state with the Di2 system in many respects. As example, they only let you set a configuration of crank or cassettes based on what they currently sell for these systems. They used to sell an 11 spd. 11-23 cassette as example, but as they no longer sell it (even if you own one) they don't allow that cassette to be used in the Di2 setup. Likewise if you were to buy an FSA 46/30 crank, you cannot enter that crank choice into the system as Shimano doesn't sell it. Big PITA in most users opinions.

They also "protect" the system in many respects and lock out certain gear choices if using Synchro or Semi. They assume you'll make what they think is a bad choice and use the smallest chainring and the smallest cog, so they lock out that selection in the system if you tell it you are using a particular crank and particular cassette. Thus a 50/34 crank with about any cassette will have the system prevent a shift to either of the 2 smallest cogs while in the smallest chainring.

You can cheat the system and tell E-Tube that you have a 53/39 crank and 12-25 cassette (when you really have a 50/34 and 11-25), the system will then let you use all the range of the cassette small/small combo's, etc... when in manual mode. The reality is you can tell E-Tube you have that crank and cassette of type A then install Type B or anything you like, it's not going to be counting the number of teeth on a ring or cog. Cheating lets you use manual mode to move across the entire cassette range typically when in manual mode. You can then and usually set the Gear Position control to Off, which releases control. About the only time not using the system you tell E-Tube is if you are using either the new bar display unit or you have Di2 connected to a Garmin where you see the gear selections on a screen. Than what you've displayed will be wrong.

When you enable Synchro or Semi, you are releasing shift control to the system. Semi will only move the rear to different gears IF you change rings up front. Full Synchro changes the front and rear IF you hit certain combo's. When you tell E-Tube the actual crank/cassette combo and define a shift map, the system figures out when the next appropriate gear is and shifts front and/or rear to get to that next gear. Your call as to whether you like or want that.

Fast/medium/slow only defines the speed the system moves during these shifts but does affect how the system responds when you do a press and hold of the buttons. Again, YMMV and you need to try different settings and find for yourself what you like.

EDIT:, And for question 3 and as far as I can see, there's no "SM1" or "SM2". Shimano shows it as "S1", "S2", or "M" for Shift modes 1 (Full Synchro), 2 (Semi) or Manual. Where are you seeing "set both SM1 and SM2 to the same shift mode (say, synchronized):.

And you are correct that the manual sucks. They do not well describe WHY you have these selections or the logic for them which makes it hard to then select one over the other.