We just got off the phone with our broker on a renewal and it is right in that range. 

If I already offered them these two options via text/phone, and I start the 60-Day notice vacate tomorrow, can they use this against me?

If you are doing it alone, why not pick up a phone and call them and be like "hey" the lease notes rent is due the first, I know there is a grace period on this but I would appreciate it if you could make the payments on the first?

The receptionist was kind enough to give me the phone number they have on file which is for Bizee, IncFile.com.

I us a property management app to receive less phone calls from tenants and collect less rent in person.I am trialing a couple others, I will be glad to let you know what I decide to go with if I find one better. 

That's probably "phone book". 

When I replied back to their email asking when I could pickup keys to assess the situation, she doesn’t respond to email, nor she pick the phone, nor responds to text.

Actually TALK TO THEM on the phone and/or in person, find out about their situation, and if they seem like a good fit, basically just be smart about it, and have human interactions with them, it's that simple. 

I would collect guest data for 1 year (phone and email) and then have a direct booking site and a marketing campaign to previous guests to book direct. 

I can't post phone numbers here but you can find them with a quick google search.