With "kilka", the verb is actually singular.
And "drzwi" being plurale tantum, needs the numeral to be a collective one. So we end up with "jest kilkoro wąskich drzwi". Which I have to say sounds pretty weird - even the natives aren't that great with collective numerals - and I guess a lot of people would say "kilka" even if it's actually incorrect.
'In your house are narrow doors'. It is not necessary to say 'there'. Or, yes, one could say' There are narrow doors in your house' but when I reverse the wording I can miss out the 'there'. Oh...never mind...I just wanted a break. These exercises aren't enough to keep the mind alive.