Hi and Welcome to the forum, you might want to have a look at the following FAQ which explains where everything is
Welcome to Benefits and Work The timescale is about what we would expect and it is not
uncommon to be offered a home visit (although some people have to fight like crazy to get one!).
The assessment will be very similar whether it is carried out in an assessment centre or the claimant's home. The PIP guide explains what to expect.
PIP help for claimants The assessor might arrive on time, early, late - or not at all! S/he will have the same rights as any other visitor to your home. It is up to you where the assessment takes place and who you have with you. The assessor does not have the right to inspect the rest of your home (although we have not heard of them asking to do so). Of course, if there is any aid or adaptation that you wish to show them that is up to you too.
May I suggest that you bookmark/favourite this on your web browser now so that you can find it easily in future? This will allow you to return with further questions or comments about your PIP without having to start a new topic each time. It helps us enormously when everything relating to the same claim is kept in one topic - and I hope you will find it useful too