Spinnors

If you want to travel to all three countries you will have to apply for all three visas. 
 
Maybe only choose one of those countries.
Requirements for France are fairly strict and she might not get the visa as a brand new resident. (think 3 months of bank statements) and of course with Schengen she will have to get travel insurance. 
I also know for the UK she will have to send her passport off to get the visa in her passport. Probably the same requirement for France. Not sure about Ireland… 

Absolutely submit the complete tax return.  As you read instructions, pay attention to little words like "or" and interpret them literally.

If she does not change her name in her Philippine passport before being issued her spouse visa, she will not be able to use her married name on her US IDs and accounts immediately after arrival.  If SSA strictly follows their policy for changing the name on a non-US citizen's SSN card, your wife would need to present a name change order from a US state court, or a new green card with her married name, or a US naturalization certificate with her new name.  So if your marriage is already PSA-registered, it would be so much less hassle to change her passport name before she gets her visa.  We talked about this also in the thread below --
 
 

For all stages of the CR1 process, PSA marriage certificate is the only acceptable documentation of legal marriage in the Philippines -- https://travel.state.gov/content/travel/en/us-visas/Visa-Reciprocity-and-Civil-Documents-by-Country/Philippines.html
 

You will need the PSA certificate. You should have asked your LCR if there is a way to expedite it. Most will expedite for a fee. But if you did not ask for expedite when it was filed you will need to wait.

1.  Your BC is not required.  You can use your Passport as evidence you are a US Citizen
2. Better to change her name now and get passport in married name.  Far better.  No brainer.  Really!
3.  No
4.  No.  I-134a is required
5. A person has one or the other.  Zip Codes are for US addresses
6.  Actual dates.  She may have lived at her same address since birth
7,  Current address.
 

G325a is an artifact from years ago.  The I-134a replaced it.  Get your information here or from the actual form instructions and you'll be on the straight and narrow.
 
Your wife only has to change her name in her passport, then her visa, green card, and all future US ID will be in the married name.  She doesn't need to change her name for any other Philippines ID, just the passport, which is only used for international travel.  Once she gets the visa and on her flight to the USA, her other Philippine ID'S become souvenirs.  If she has a PI driver license she can use that when she visits or her US license.