Working Visa, Job type

Hello everyone,

So I have been living for 4 years in Japan now (Exchange Student, Working Holiday and 2 years working at a company). A lot of things have been going really badly the last few months.
I was going to marry my now ex-boyfriend, but things did not work out... and the company I had been working for for 2 years is about to go bankrupt, so I had to leave a few days ago (we discussed the matter together, that was the best solution for both sides)
So theoretically I got another 3 month to find a new job, but actually my Visa is going to expire mid of August, so technically I only have another 2 months.
I have been living here for 4 years and built up a really nice life. I do not think that I will have big problems finding a new job as I speak Japanese fluently and have a Bachelors Degree for Science. But actually I kind of found out what I really want to work as and I kind of hope that I can do freelance in future. So now I am thinking about how I can make this happen. So I got a few questions, I hope someone can help me out!

I know that I need a job to be able to renew my Visa, but do I have to find a job that I can begin before my Visa expires or is it sufficient if for example I find a job until mid of August but can only start in October (you know how some companies only hire on certain dates) Would that company be able to get my Visa renewed in time?
Or would I have to change to a tourist visa in the meanwhile and apply from zero? That would make things quite a hassle I guess?
Also, do I need to have a full time job? I always thought I need to be a full-time 正社員 to get a Visa, but I have read a few times on the internet about people who claim they only work part-time but receive the minimum of 200.000Y stated somewhere, so their immigration office accepted.

Is there anyone who experienced this situation? I hope you can give me some advice! I would really appreciate any help. I really want to stay :(

You must do one of those three things before your current status expires:

1. Apply for an extension of period of stay.
2. Apply for a change of status.
3. Leave.

You do 1 if you find a new job which falls under the same status as your current one, and 2 if it's under another, assuming of course thqt you fulfill all the requirements. I do not know if it is possible to apply in August if your new job would start in October, but it seems to be worth a try if the starting day of your new job is still within the two-month "grace period".