Hi Cathy, I'd trust my gut instinct and continue to say no. I have been hosting for 6 minths and I too found it a little uncomfortable to say no at first. So I offered info re other, more suitable places in the area. I have a cost per 2pp and a surcharge for any more people staying. Utilities costs become higher and wear and tear is a consideration. Personally, I wouldn't feel comfortable with anyone staying at my place for 4 months with plans to bring friends, that I knew nothing about, to stay.
They might stay for extended periods or w'ends, either way its a bit too loose of an arrangement
for me. Good luck