Yes, Newark still does same day oath ceremonies.

You need to meet 3 of the criteria. Job letters alone is not sufficient. Should evaluate yourself based on those criteria and then ask an attorney...

If your spouse is a US Citizen, you are eligible and OK to file for adjustment of status. If not, then I would not recommend it.

The wait time for an H4 visa in Singapore is 3 days, why not just go and get it done?

Sure, a copy or the attorney copy would be enough.

I do not see any issue with this approach. Once you're I-140 is approved you'll have to process through the US consulate in Canada in order to...

You certainly could come back on ESTA. As for your OPT issue, you can try reaching out to an attorney on AILA who focuses on that subject....

As long as you are in status when you try and change status you are good to wait for the application to be adjudicated.

London is not currently allowing people to make an appointment for an E2 interview. Going to be a long wait.

The US Government will not stop you from leaving, only from returning.