Hey Maria. I'm a SFH investor in the Sacramento suburbs and do the same thing that you're proposing. I take quality pictures and ask that anyone who is interested in the house to first drive by the area and make sure the neighborhood fits their needs. Then, if they're interested in seeing the inside, they need to meet my requirements and fill out an application.
Anyone who applies and doesn't meet my requirements gets a short email letting them know that they didn't meet the requirements for the property. Everyone who did meet the requirements gets a date and time to show up and see the inside of the place. I usually schedule everyone for the same 90 minute window so that I don't have to wait around for no-shows and waste too much time.
To answer your questions:
1) No need to really sugarcoat this. I simply let people know that I have too many people interested in the property and I don't have time to show it repeatedly. There will be a showing for those who have filled out an application and meet all of the minimum selection criteria.
2) If someone doesn't qualify, let them know early so they don't waste their time waiting for you.
3) Yes, there is nothing illegal about discriminating against tenants who don't meet your minimum selection criteria as long as you consistently apply your requirements across all applicants. The entire point of screening is to discriminate against those who don't meet the requirements so that you can minimize future headaches and protect your investment.
For the tenant who already applied before you put up minimum requirements, I would probably refund their application fee and not show them the place. If someone before applying tells me something that I know would disqualify them from being selected to rent the place I usually encourage them not to waste their money on application fees.
Hope this helps!