Here's some forum threads with good information to help with the passport questions for your children:-

http://filipinaroses.com/showthread....Child+passport

http://filipinaroses.com/showthread....Child+passport

http://filipinaroses.com/showthread....er-please-help

http://filipinaroses.com/showthread....Child+passport

Regarding the spouse visa application, your wife can only make application based on the details in her valid passport. If her passport does not show her married name then she cannot apply using that.

There are some key documents that must be submitted together with the visa application.
Without these documents the application will not be accepted.
She will need to secure an pass certificate in English Language from an approved source listed on the UKBA approved listing. The details can be found here English language requirement
Additionally she will need a certificate of TB screening, again from the UKBA approved clinic in Manila. The details can be found here Tuberculosis testing in the Philippines
Be aware the the TB certificate is only valid for 6 months.

May I suggest you review the forum thread here called All New Guide - How to apply for a Spouse/Partner Visa
Hopefully it will give good background information on the evidential documentation needed and also provide links to the UKBA webpages.

Another useful link is here called Applying for a UK visa in the Philippines Be sure to follow the links contained within also.

Regarding the needed CFO 'sticker' your wife is able to undertake the seminar at any convenient time. Many folks schedule it at the same time as other activities in Manila etc.
Be aware that she will be unable to secure the actual passport sticker until her UK visa becomes valid. For that reason many folks also wait until they have the visa before taking the seminar then they receive the sticker on the same day. It's a personal choice.

We do have a number of members here have followed the same path as that needed by your stepson
I'm sure some will drop by soon.
In the meantime try to do a search here.

It's often not quite as straightforward as when the father is not mentioned on the Birth Certificate, but can be done.....just a little more attention needed.

If I have time I'll look out the threads for you.

Don't be shy to continue asking clarifications