@Martina379, I think these are all legitimate questions and concerns, which we all deal with in one form or another.
As you do, I also exchange messages with guests before accepting them. I almost always am able to immediately respond to a request or inquiry and I send my 'inquiry response message' where I thank them for their inquiry or request and lay out my policies, to which I ask them to respond saying they agree so I can approve them for their stay.
Most respond very quickly and I am able to approve them within 20 or 30 minutes usually. I have had only two people who have not responded and the clock continued to count down, so after several hours I explain to them that I'm not rushing them, but per AirBnb, we have 24 hours to confirm the booking or I will be forced to deny the request. One withdrew the request without messaging me, so I knew that person would not have been a good fit for my place. The other one never replied, so I had to deny her.
Following this, I have a 100% response rate.
For your second question, yes, letting people into our space without any prior information can be cause for concern. I have had a few newbies who had nothing at all on their profile. I ask welcome them to AirBnb and explain that almost all hosts will ask them to complete their profile, getting some verifications, adding a photo and some personal info.
I don't think it's appropriate and probably against AirBnb policy to ask for personal info such as last names. However, after they book and confirmed, you can see their last name and city. I usually Google the person and can find their info, including where they work and such.
I'd say in general, make sure your rules are clear in your listing and in your 'inquiry response' message, which I feel can discourage 'bad' guests from booking in many cases.