As per the provisions of the law, the assessee should purchase a house one year before or two years after the sale or construct the house within 3 years of sale. As per your queries,
* Section 54F does not allow construction of house after three years of transfer but within three years of transfer
* If you are unable to invest the sale proceeds equivalent to the amount of capital gains in purchase or construction of the house property till the due date of filling of your return, you are required by law to invest the same in capital gains investment scheme before such due date
* Exemption u/s 54F may be granted if the construction of house started before the sale of the said house property, provided your case is bona fide and you have proof of investing the whole amount in the construction of your house.
You can refer to the decided case law of CIT v/s H.K. Kapoor (12 August 1997) for clarity on your last query