In the refrigerator it will be fine for 5 or 6 days, at room temp its only good for 8 hours absolute max, even then make sure you're cooking it to an internal temperature of 165 F to kill any bacteria.
Yes it is safe to cook a partially defrosted chicken if the entire chicken gets cooked; which will take longer if the center is still frozen when you start cooking it compared to the time it would take if the chicken was raw or completely defrosted. The primary concerns you have with chicken are campylobacter (bacteria) which are not rendered harmless until they have experienced 68°C (155°F) for at least a few minutes. It's always safer to completely defrost before cooking, unless you enjoys taking risks with your health...
Yes, you can thaw, cook, and refreeze chicken.
It's safe as long as you cook the chicken to 160 degrees F.
This will depend on how long the chicken was left at 69 degrees. Ideally the chicken would have been defrosted to only 40-45 degrees then cooked fully to a minimum of 170 degrees. If the chicken has been over 45 degrees for more than a few hours, I would suggest not eating it at all.
no
No. It is not safe.
If your chicken has white dots on it, you should visit the doctor and get that checked out
No, not unless frozen.
You can use glassware or any microwave-safe dish to cook chicken in the microwave. Check the bottom of any plastic dishes to see if they are microwave-safe.
If you are asking "Can chicken that has been frozen be defrosted and cooked?" then the answer is yes. If you are asking if chicken that has been frozen, defrosted, refrozen and defrosted again can be cooked than the answer is yes but it's not safe. When you freeze food water crystals expand and damage cells. When you defrost your food, particularly if you leave it on the counter instead of in the fridge bacteria causing microorganisms have the chance to multiple. When you then refreeze it even larger ice crystals are formed destroying even more cell membranes. After this you defrost it again and the microorganisms from before can double. Usually at this point the meat doesn't look or smell so great.
Of course
As long as the chicken was thoroughly cooked and reached the appropriate temperature in all parts of the chicken, it should be safe to eat.