Spouse visa about to expire

I have been issued a spouse visa for one year. I arrived in Japan June 4 last year and got pregnant and since my husband is very busy at work, we both decided I go home and have our baby born in the Philippines. I already have my return ticket to Japan scheduled on May 14. My question is:
1. Will 3 weeks time be enough to process my visa extension?
2. And how long does it normally take to have my visa processed? The plan is to go back to the Philippines as soon as I have my visa renewed/extended so I can work on my child's documents and so I can take her with me to Japan the soonest time possible. As for now, I still don't have enough time to process everything since I just delivered via c-section last March and still need time to rest.
3. Would you advise if I just let my visa expire and just request for a new COE together with my child?
4. Or would you advise if I try to enter under visa waiver system and apply for change status once inside Japan? And how do we go about that?

Japanese immigration does not look kindly on people who are on spouse status but do not actually live with their Japanese spouse (because that's supposed to be the reason why you applied for it). Worse, you were only given a one-year period of stay, which is already a bad sign, and you spent a significant part of that away from your spouse. And then you plan to leave *again*?

If I were you, I woild not come back to Japan until everything is in order so you can actually live with your spouse as you are supposed to.

1 & 2. You never know. In the first place, can you gather all the documents required (like the resident's register, your Japanese husband's family registry showing his marriage to you, his income/tax paper, etc.) quickly and file for extension of your "spouse of Japanese national" status? Once you get the "under processing" stamp, it might be ready in a few weeks, but you never know.

Also, since the immigration authorities will be able to tell from your resident's register (or from your passport) that you have not been living in Japan for most of the past one year, you should have a very good explanation about why you've been away so long. C-section is a big thing, I know, but you say this was just this March. Before that, you left Japan in June or so of last year, and have been away from your husband for many months.

3. And start from zero? If you let it expire, the authorities might think that you did not even "care to" extend the status; you apply again, and they will ask you questions why you did not stay together in Japan, and why now coming to Japan so soon. Your husband and you together need to have a good explanation about why you've been separated so long, and how you plan to stay in Japan together in the future.

Getting only one year "spouse" status when you apply for that status the first time is not uncommon, but letting it expire might be a warning sign for them.

4. Is the visa waiver system available to Filipinos?

On a different note, what passport your new born has? Have you taken care of registration of your child with Japanese embassy in the Philipines since the child is born outside Japan?

There were posts here recently where child born to Japanese father in Philipines was not registered within an year and now does not have a nationality

1. Will 3 weeks time be enough to process my visa extension?

According the immigration office website, visa renewal process duration takes from two weeks to three months. So, the answer to your question is, YES 3 weeks is enough. You should do this as soon as possible. It is not too late.

As for the rest of your questions, you have got above some of great replies.
Your case sounds extremely suspicious to me as well.
Those who are under marriage visa MUST be together with their spouse. It makes no sense to have a Japanese Spouse visa while being separated with your Japanese spouse. I doubt that your visa renewal will be denied but I am almost sure that they will grant you either 6 months or the max 1 year. This also should affect your future visa renewals as well. Your marriage life does not sound stable.

By the way, there are cases where they can renew your visa without any problems even under these situations. It depends on how long have you been married to your husband before coming to Japan. How long did you live with husband in your country? the type of job your husband do? and so on.