@Yangyang Jin Where is your property located? Depending on where, I might be able to give you better insights as to how showings should be progressing.
To answer your questions, we, as realtors, do not get to limit where our listings are getting syndicated to. There is however, some places that you need to list it separately in order to get traffic there as well.
I do not agree with filling out paperwork prior to touring a unit. There are several ways in which landlords want their perspective tenants apply for a rental and it doesn't make sense to go through the application process prior to seeing a property. Plus, there's a ton of scammers out there that ask the same of renters, so I advise anyone that calls me to avoid filling out anything prior to actually touring.
You can very easily vet everyone over the phone, which is what I do with everyone that calls me prior to scheduling a tour.
You may want to look for someone else to list your rentals. Depending on where it is, I may be able to help and if can't personally, I can probably refer you to someone who can.