For ceramic tile, you need a solid subfloor that won't flex, etc. They generally recommend 1 1/8" thick. I would just put 3/4" cement board on the subfloor which would make a perfect underlayment for the tile. You could use a 1/2" exterior glue plywood such as cdx if you want.
The 3/4" you have is fine for under carpet. Assuming 16" center joists and it is nailed/screwed/glued down properly. Only add another 1/2" to stiffen it up if the floor flexes or bounces more than you like when walking on it.
I wouldn't be concerned about the gray color (except that it indicates getting wet) but check to see if the OSB is damaged. If so then replace. Jab it with a screwdriver or something all over the area that got wet to see if any of the chipped board is damaged or loose or rotted. OSB can get wet and dry and still be ok but it depends upon how wet and how long it was wet before you see damage to the wood or glue. Jump up and down on it (your kids will if you don't) and it if feels solid and you don't fall through, then you may be ok. If you fall through to the first floor, then replace it when you get out of the hospital. (I'm not sure if you want to be straddling a joist when you try that or not).
If it is still solid, then walk on it and look at the warpage. You will want it flat for hardwood floors but carpet and pad may absorb some unevenness but you might try some pad and carpet to see if it bothers you or not(I can't tell from here). If it bothers you then replace it or cover it all with 1/2".
We usually allow for the bottom of the door to be 1 1/4" above the unfinished floor for carpets (with a 1/2" pad and 1/2" carpet)(unless you know you are going with a tall carpet). Pick out your carpet before installing the doors. Maybe a little higher for tile if you are adding a backer board that would bring it up higher than the carpet. Good luck.