A few edits (spelling) - my legal-eagle-eye proofreader coming out:

Allow new cat a minimum of four hours to investigate the room. Do not be surprised after reentering room to have lost the new cat.

Confirm existence of the new cat by monitoring the level of food/water bowls and checking for paw prints or deposits in the litter tray.

In the meantime the resident cats will have smelled (smelt is a fish) that there is someone new in the house.

Our cats usually ignore the spare room for a couple of days, hoping no "e" in hoping that the new cat will leave !!!

By this stage our resident cats are usually playing paws with the new cat under the door. i.e. They take turns sticking their paws under the door and the new cat of the other side of the door smack the paw !!!

Wait until until the new cat is comfortable enough to want to leave the spare room. This can vary a lot Treacle wanted out after 30 minutes, whereas (one word) our latest cat 6 year old Sandy stayed in there happily for four weeks.

The average is about a week but it is important not to rush this stage, the new cat must feel confident enough to want to interact with the house and other residents.

Monitor the fighting but do not interfere unless blood is spilt ? a British-ism?, cats need to find their natural place in the household in this way.

Looks good! Thanks for doing this!