While normal white discharge is common in many women, but if it is heavy and with odour then there may be an underlying infection like yeast or bacterial vaginosis, which is a form of vaginal infection. It is essential that you see a gynecologist or an expert in sexually transmitted infections so that you can get the right diagnosis and treatment.

Menstrual cycles can sometimes vary in length and its common and nothing to worry about. However, if there is a possibility of pregnancy it's important to consider that as a potential cause. Get tested to confirm. 

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If you are not getting your periods on time then do consult the gynecologist. This may be due to different reasons such as stress, hormonal imbalance or underlying medical conditions. 

Maybe you have a yeast infection. Symptoms such as itching, smelly discharge, and discomfort in the vaginal area are the common ones that affect women. Besides the vaginal region and inside the thighs, fungal infections can also affect the mouth, throat, and skin. The clothes can be attributed to such infections as well. Firstly, there are the unwanted side effects of some medications. Prevention of yeast infections should be made by cotton underwear while avoiding scented items to the extent that OTC antifungal creams should be used.

That is not possible. Your late periods may be due to hormonal changes or stress.