About fluoxetine tablets - what is best time to take them and with or without food?

First off you really need to take things one step at a time and calm yourself down in order to start your road to "recovery", stressing situations will only make things worse for you and I know panic attacks are awful, so relax, you can not go on living in constant fear, you must have FAITH that all aspects in your life are about to start improving as you will start to pave YOUR road to recovery.
Having said that I was on Fluoxetine and it did help me quite well to overcome many conditions, like anxiety, intrusive thoughts, so I know where you are coming from but starting a treatment with fear is not the way to go. Plus you got 2 beautiful angels to look forward to and that should be a great motivation for you.

Fluoxetine can be taken with or without food, regarding the time you should take it as prescribed, a word of advice... trial and error:

Somnolence is considered a very common side effect affecting 17% and dizziness up to 11% of people taking this antidepressant and on the other hand insomnia is also considered a very common side effect affecting up to 33% of people taking this med.
So, you will have to try and see what suits you best according to the potential side effects I mentioned, if you can not sleep take it in the AM and if you become sedated/sleepy/dizzy at night, this is trial and error.
You will start to feel better within the first 2 weeks, and for its full therapeutic benefit it may take 4 to 6 weeks, remember everyone reacts differently to medications, be patient, you will have good days and bad days, and it is normal as your organism is adapting to the medication and always consult with your Dr./Psychiatrist if in doubt.