Can a fibroadenoma develop into cancer?

No. Fibroadenomas don't turn into breast cancer, which is a good thing because they are very common!
Possibly. Fibroadenoma of which organ? If breast: not usually. However, cancer can develop within the fibroadenoma and therefore you can have ductal carcinoma in situ or invasive carcinoma develop within the adenoma. The fibroadenoma, per se, though is not transforming. Fibroadenoma is on a spectrum with phyllodes tumor, the spectrum of which includes malignant phyllodes tumore.
Yes, small risk. Fibroadenomas are associated with a small increased risk of developing breast cancer, approximately 1.5 to 2 times that of the general population. ( based on prospective study in benign breast cancer - published in jama and nejm).
No. Fibroadenomas of the breast can remain for years without becoming cancerous.
But beware. In some patients a fibroadenoma can grow to a large size and become something called phylloides tumor. These are usually benign but have a "malignant potential." for this reason it is better to remove fibroadenoma tumors if they don't spontaneously regress after a woman passes her mid-twenties.