OK, my 2 eurocents' worth - and for the 73CL
1) BAT on - check voltage - STANDBY POWER switch to BAT - check you have both BAT bus voltage, SBY DC voltage, SBY AC volts + freq and INV volts + freq. Then select STANDBY POWER switch back to AUTO and proceed with normal preparation, i.e. either do the firetest & start the APU or connect the GPU.
2) For the same reason that auto-go-around is not available during a single-channel CAT1-approach - there is only one channel engaged, and therefore Boeing doesn't seem to like the idea that just one auto-pilot flies away happily without another auto-pilot to compare & check what's going on...
3) Depends on mass (and therefore variant), have a look in the QRP or use the FMC HOLD-page to predict holding cabability. However, for the -300 typical approach masses, you can use 45 kg/min. or 2,7T/hr as a consevative guideline. Add 10% for LEDs extended and 50% for gear extended
NB guidelines only - don't you & your lawyers come running if you run out of fuel
4) It starts way before you go around @ your destination - if the WX looks as though it's gonna be tight & a diversion might need to be performed, you make a point of covering the following in your approach brief (along all the oter stuff, of course...):
a) WX at alternate must be good enough to allow a few margins - if you're no longer comfy with your alternate, nominate another one while you still have the fuel. If contamination might affect the usability of the alternate, remember to allow time for snow-clearing - or, preferably, find another one.
b) Minimum fuel for diversion - this one needs to be carved in stone, it's a contract between the 2 crewmembers that
"When we hit (e.g.) 2200 kg - unless we have a runway visual in front of us and are cleared to land - we divert, no ifs, no buts, nomatter where we are in the approach!". Make sure your companys flightplans take the direction of the missed approach into account - e.g. LPA rwy 03 with alternate TFS using rwy 08 - if the plog says 600 kgs., you must go "Yeah, right...whatever...I'll call that 1200 kg.for comfort, thank you very much" (LPA 03 MAP goes to the NE by about 40 NM, TFS is WSW of LPA).
c) Taking b) into account - how much holding cabability do you have? Is it worth holding out till you need to divert, or if they come up with a tight EAT will you divert straight away? (and thus maybe be the first on the ground on the alternate, beating all the heroes who hold & hold till their eyes water and they need to go, right now!). There can be benefits in diverting early, especially if the wx appears to be improving - chances are everybody else is also using the same alternate, so you'll be first in the queue for ramp space, fuel & handling - that'll mean that you're first out again when your destination re-opens. Oh, and you won't be the last guy diverting, only to hear the words at the alternate "Ground is full, go away!"

Also look at things like when the airport closes, when the firecover drops below the category you require, when the fuellers go home etc. etc. - all these might dictate that you divert while you still have plenty of fuel in the tanks.
d) The planned routing & requested level to the alternate, and a brief look at the expected arrival & approach (so they don't chatch you out, especially if the alternate is near the destination - the diversion might only be 10 min. flight from when you hit TOGA, so no time to be clueless).
e) If time allows, have PM call the approach unit at the alternate airport and ask "If we came by in 20 min. - what would the traffic be"? If the ATCO starts laughing and and says "Think of a number between 10 and 18"

- then you need a plan C, fast!
f) Get on to the company via ACARS or via the handling agent (or - if further afield - via HF phonepatch) and ask them for their preferences if more than one alternate might be usable. If they are alerted well in advance, a good ops will have the handling organised, have a new flightplan in the system, or have organised coaches, hotac, engineering support and all the other goodies you might need.
g) When it's chrunch-time, tell ATC a couple of minutes i advance that you're requesting clearance to XXX at FL NNN via XZY. Fly the last holding lap in HDG SEL and raw data while PM prepares the FMC. This is done by going to RTE page 1 and inserting you alternate as the new destination. From there on, you can select the arrivals & approaches as you normally do.
h) And finally - make the mental note that once you hit Final Reserve Fuel, you'll yell MAYDAY loud & clear & get that priority. Better advise ATC like, 5 minutes before it gets really critical - they don't mind-read (despite the fact it sometimes seems so

) When you reach the point where you have doubt that fuel remains for another approach - make sure to brief accordingly, it's way better to crash during a less-than-perfect autoland inside the fence than it is to glide to a random crash-site outside the fence.
I have without doubt forgotten a really important point, I'll leave it to the next posters to correct me.
Hope this helps - cheers fm
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