what happens to the building itself or the rights to it, if the lease term expires and no options taken

If you are leasing the building and your lease ends the building remains with the owner. If you want to stay you should have notified the owner 60- 180 days in advance in order to try and renegotiate your lease. If the owner does not want to, there's little you can do except move, or become a holdover. However staying without a lease is an expensive and not suggested method of staying. It's better to ask for a month to month lease until you find a new space.

A lot will be answered - typically - by the language in the lease document. It generally will contain specifics as to the lease term expiring and what happens afterward. Typically holding over on a month to month lease will be at a much greater amount of rent. If a tenant - or landlord - does not move, prior to the end of the lease term, to negotiate a renewal or a continuation of the lease in some form or fashion then the tenant will be in a holdover position and subject to the landlord leasing the space to someone else.

Dear Arjun S.,
Carefully read the lease. Better yet, consult with both a competent commercial broker and your attorney, preferably the one that represented you when the lease was signed. There are too many variables to answer your question in a meaningful way. Good Luck.