Desperately Seeking Sewage Solace 2 Part Question

[shnabbles]

Howdy. Thanks for any and all advice.

1. Terrible issues with my plumbing lately via the toilet.
It doesn't happen all the time, but at some point, the upstairs toilet will back up, causing gurgling in the nearby sink & shower drains. The water will go to the crack in my unfinished floor ( I know) and cascade like gentle rain from a tropical jungle through the kitchen ceiling below.
I currently have the toilet off. Really want to know what happened to one of the toilet screws that vanished in the process, but that's beside the point. I've snaked it until I could snake it no more and all I got was a clump of hair with a very thin rubber band holding the hair in place. I just don't think this clump was the cause of all my problems. Obviously, I have many problems.
What can be causing this? It seems to happen in cycles where the toilet will flush fine for sometimes weeks and then inevitably bring the storm. I can feel air coming through the pipe, so my trap somewhere up on the roof is doing it's job. Could bad piping from the sink cause some sort of vacuum issue? (Working on that too.)

2. The toilet sits on an unfinished tile floor from when my plumber friend started doing the floor and then suddenly stopped 4 years ago without any reason even though I've asked him in person. (Yes, I paid and am probably TOO easy going when it comes to contracting) I don't know how to tile the floor and no longer have the funds to hire someone.
The tiles cracked and came loose underneath the toilet. I have this idea of some kind of NOT-tile that would sit nicely underneath a toilet. It would be tile-LIKE, but maybe have a little give to it and be easy to clean and hard to crack. I would then tile AROUND that. It would be like the red rectangle in the attached pic.
What would be a superior product to use for this idea?

 

[Reach4]

1. Terrible issues with my plumbing lately via the toilet.
It doesn't happen all the time, but at some point, the upstairs toilet will back up, causing gurgling in the nearby sink & shower drains. The water will go to the crack in my unfinished floor ( I know) and cascade like gentle rain from a tropical jungle through the kitchen ceiling below.
I currently have the toilet off. Really want to know what happened to one of the toilet screws that vanished in the process, but that's beside the point. I've snaked it until I could snake it no more and all I got was a clump of hair with a very thin rubber band holding the hair in place. I just don't think this clump was the cause of all my problems.

You may want to have a drain cleaning professional use a big snake. The little one can poke thru a blockage.

There is a second problem: the wax has failed. That can happen because you plunge, but the drain below is clogged, rather than the clog being in the toilet trapway.

2. The toilet sits on an unfinished tile floor from when my plumber friend started doing the floor and then suddenly stopped 4 years ago without any reason even though I've asked him in person. (Yes, I paid and am probably TOO easy going when it comes to contracting) I don't know how to tile the floor and no longer have the funds to hire someone.
The tiles cracked and came loose underneath the toilet. I have this idea of some kind of NOT-tile that would sit nicely underneath a toilet. It would be tile-LIKE, but maybe have a little give to it and be easy to clean and hard to crack. I would then tile AROUND that. It would be like the red rectangle in the attached pic.
What would be a superior product to use for this idea?

I think I understand. Your tile around the toilet does not look good. You want a finishing plate/spacer of some sort.
Try this search in a search engine: toilet base plate
https://www.google.com/search?q=toilet+base+plate&source=lnms&tbm=isch&sa=X

You don't want a toilet to rock, so you would not want the base plate to give.

 

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[shnabbles]

That definitely answers the 2nd question! I knew I couldn't be the first to think of such an implement, but had no idea what it was called.
I like the idea of the one pictured below. Something nice and sturdy. I'd think there would be more of them though. Most seem to come in this oval pre-cut like the 2nd picture.

 

[shnabbles]

Also did not see your initial answer. I will look into getting a drain pipe cleaner guy. Admittedly, the snake I was using was a pretty basic one from the hardware store.

 

[Reach4]

I think you can get pedestals/base plates in marble. I don't know if you have a marble place cut them, or if they are standard.

While some are grossed out by the idea of a carpet near a toilet, they can be good if the guys are willing to set. You can cut to size.

When you get your toilet re-set with new wax, the toilet gets set down without wax first. The shims that prevent rocking are placed, toilet gets lifted, wax is set on the ring, and the toilet is dropped.

There are waxless units that will probably survive plunging into a clogged drain better than wax. But getting rid of the clog is the deal. Most modern toilets seldom need a plunger.