Parquet floors do not buckle,the worst that can happen is some of the pieces of wood may come adrift,just check the stability of the floor before carpeting. Take into consideration that bitumen will trap moisture which can cause discolouration of carpets all though instances are rare.
It is not clear what you want to achieve,use a scrubbing brush and water with a mild soap.I can see one floor is tile but the other looks like stone.Glazed tiles are ok to take a washing with brick cleaner if there is old mortar stains while the if they are,stone tiles should just need a good scrubb...
prize off the hinge covers and you will see a number of fixings,just take them all out until the door drops off or the hinges that are on the door frame may be best,take off the covers and see,you might need an allen key.
