Both of your questions have been well answered. The hole in the back very likely had a combination blade guard, splitter and anti kickback pawl contraption that is so unwieldy that they are often removed after making the first few cuts. Mine is in a bin with other rarely used table saw attachments.

Your throat plate has too wide of a slot for the blade. It was possibly made for a dado or shaper blade. Make a new one out of wood or plastic and then raise the blade up through it to make the perfect size slot. What you have now is asking for a kickback if you are ripping a narrow piece.

Years ago a kickback broke through a fingernail and put a hole my finger that exposed the bone. X-rays showed the end bone of my road rage finger was in 7 pieces. The emergency room had to call in an Ortho specialist to line everything up and splint it. Not fun. To this day that finger nail looks a little odd. Years before that episode a kickback hit me in the chest pretty hard. I remember thinking it was a good thing that piece wasn't mitered on the end.

Saw Safety Tips:. Some learned the hard way.
Caution when cutting short and/or narrow pieces. They can get cocked between the blade and the fence and get spit out.
Use chicken sticks when you can. I keep several near the saw at all times.
I use the table saw for rips and sheet goods. I hardly ever use my miter gauge. It hangs on the wall. Cross cuts and miters are so much easier and safer with a good sliding power miter saw.
If you ever need to use a radial arm saw DO NOT rip with it. It is an accident waiting to happen. Only use it like it is an old fashioned sliding power miter saw. Just because you can rip with it does not mean you should. Just don't.