Deputy Purple

Yes, you can and should file both petitions in the same envelope but with separate cover letters and checks. Two stacks, one envelope.

I've been a Single Father since before my youngest daughter's 3rd birthday. Their mother was present (around the edges of their lives so to speak) but never in the role of a parent. Those 10 years of my life would have been a lot easier if I just let her have my daughters and paid her Child Support but that would not have been in my daughters' best interest. Your assumptions that his motives are not the best interest of the child are as bad as assuming that the mother is a bad Mom.
It would be prudent to prevent international travel of the child until a family court decides matters of physical custody.
That I agree with, lock, stock & barrel...

What is important is what was required when you registered to vote.
As an LPR you can't vote in Federal Elections as they require you to be a US Citizen.
You may register & even vote in local and state elections unless they also require you to be a US Citizen.
There should be information on your voter's registration card, contact them and see if your registration is in violation of this.

An overstay has to be at least 180 days to result in an automatic ban. On the other hand, your overstay is not going to make it any easier for you to get another B2 visa, especially considering you needed a 212(h) waiver to get the first one.
Ok, what your attorney suggested was Russian roulette. It would have been perfectly legal for you to marry your fiance in the US. The spouse of a US citizen IS eligible to apply for a green card while they are in the US, however, there are some conditions attached. One of those conditions is that you did not intend to immigrate when you entered with your non-immigrant visa. Let's be clear that what really matters here is what USCIS thinks your intention was, and not what your intention really was. If they conclude you intended to immigrate, based on the fact that you came to be with your fiance, and had done so previously, then they would have denied your green card application. Further, you would probably have been found to be guilty of material misrepresentation; i.e., lying on your green card application. The consequences are deportation and a possible lifetime ban from the US. This is why I say it's Russian roulette - it's possible to marry in the US and apply for a green card, but there is considerable risk if you fail. This risk doesn't exist if you enter the US with a visa intended to permit you to marry and apply for a green card.
If you needed a waiver for the B2, then you'll probably also need a waiver for the K1. Since you qualified on your own for the waiver with the B2 visa, you should be able to qualify on your own with the K1, as well. I presume you qualify because it's been more than 15 years since the offense. If it had been less than 15 years then your fiance would probably need to ask for a waiver on your behalf, based on his own hardship.
Your fiance's financial status may be a problem. He will have to provide an affidavit of support for you. The general requirement is that he must have income equal or higher than 125% of the poverty guidelines for his household size, which will include you. If it's only you and him, then he would need an annual income of a little over $18K. If he gets SSDI then that income can be counted. On the other hand, if he gets SSI then it can't be counted. If he can't meet the income requirements, then he'll need to find a co-sponsor who qualifies.

Are you aware of just how difficult it is for a pretty young female from the Philippines to get a Visitors Visa? You'll have to demonstrate that you have very strong reasons to return to the Philippines such as a very good job, owning land & businesses etc. Having a USC boyfriend/fiancé will actually work against you as it is a compelling reason for you to overstay or try to marry him and adjust status without returning to the Philippines.
You'd be better of just applying for the K-1 after he returns to the US.

One of my fondest memories of my time in the Philippines:
We made several trips to the local market in Paniqui. At 6ft plus in height I towered above everyone else there. She kept on forgetting that I was a "Stranger in a strange land" and just went about business as usual, I had to try to keep up as best as I could!
Once I lost track of her, just another short brown person with straight black hair in a sea of them! So I just stopped and looked around hoping to stop her. After a short {pun intended} while I felt a tapping on my chest {or maybe stomach} so I looked down to see her looking up at me!

And you're getting good advice.
Think about it, if it looks suspicious here how do you think USCIS employees will view it.
There are laws to prevent someone from entering on a Non-Immigrant Visa and adjusting to immigrant. The requirements for said visas are different.
It isn't uncommon for Alien Spouses of US Citizens to be denied Visitor's Visas or even turned back at the Port of Entry because of suspicion of immigrant intent.
If you are 100% confident that you can convince a complete stranger that your intent upon entry was to return to Hong Kong then go ahead and file for Adjustment. Just be aware that there is no room of Appeal if denied you may be hit with a charge of misrepresentation which would result in a lifetime entry ban.
Personally I wouldn't risk it even if I had a 90% chance of success because that 10% chance is too much of a risk when it comes to being with my wife.

I agree with you about not leaving the US as overstay will be forgiven upon approval of AOS.
I don't understand why you associate AOS to CR-1 Visa though. CR-1 is an Immigrant Vias and upon use the beneficiary is issued a 2 year conditional greencard so their next process is ROC (Removal of Conditions) 21 months later.

And you're getting good advice.
Think about it, if it looks suspicious here how do you think USCIS employees will view it.
There are laws to prevent someone from entering on a Non-Immigrant Visa and adjusting to immigrant. The requirements for said visas are different.
It isn't uncommon for Alien Spouses of US Citizens to be denied Visitor's Visas or even turned back at the Port of Entry because of suspicion of immigrant intent.
If you are 100% confident that you can convince a complete stranger that your intent upon entry was to return to Hong Kong then go ahead and file for Adjustment. Just be aware that there is no room of Appeal if denied you may be hit with a charge of misrepresentation which would result in a lifetime entry ban.
Personally I wouldn't risk it even if I had a 90% chance of success because that 10% chance is too much of a risk when it comes to being with my wife.

No. CR-1 is a visa to ENTER to US.
Adjusting from the F1 to conditional LPR (Lawful Permanent Resident) is what you're doing.

This response is correct for Manila but virtually nowhere else. Child custody and permission issues require country specific answers.

Who are you Jesus of Visajourney??

At the I-130 Petition stage all we provided was a copy of our Marriage Contract (certificate) and a bank statement from each of our 2 joint bank accounts (one in the Philippines and one in the US).
The chat/phone logs and other stuff like that was a ll prepared for the interview stage but never asked for.
FWIW, the child doesn't prove anything about your relationship beyond the fact that you had sex at least once. Doesn't hurt to provide documents of the child's existence but you've already had to prove the parental relationship for the baby's CRBA & US Passport, right?