The washing machines are in the kitchen because there are no other rooms in which to put them. Most properties do not have a separate utility room, so the kitchen is the only room in the house where a washing machine can be installed.
Many people do not have a dryer because they either do not have anywhere to put one or they don't agree with having one (i.e. they use too much energy). Some have combined washer/dryers, but generally dryers are a bit of a luxury... so people will dry their clothes on radiators or free-standing airers (or outside on a washing line if they have a garden).
Be aware that UK properties, especially in or near London, are very small compared to US properties. The average 2-floor, 3-bedroom family home in the UK is about 800 to 900 square feet.
I've been looking for rentals on Rightmove, is there another preferred site to use?
I use Rightmove to start with, but when I find properties I like, I will go to the website of the actual letting agent for further details. Sometimes the properties on Rightmove may not be available anymore but haven't been removed from the search listing yet.
What are Tenants admin fees?
Usually when you apply for a property you have to pay an application fee and sometimes further admin fees to cover things like processing the tenancy application, getting references, checking in and out of the property when you move etc. - in my experience, the fees are usually £100-200. I'm assuming that's what they mean by 'tenants admin fees'.
What is an extra room tax?
I don't know all the details of it but it's to do with people who claim housing benefits from the government having to pay extra money to the government if they have a spare bedroom in their property. If you are not a UK citizen, it will be illegal for you to claim government benefits anyway, so in that case, it won't apply to you.