The first situation is how speed mechanics work in Pokemon. A simply way I calculate it is to divide by 4, but multiplying by 0.25 (25%) gives the same answer. The final speed stat of your Mega-Charizard-X should be 123.
As for the second situation, I'm assuming you're multiplying the speed stat before stat modifiers? But the way you explain it is that you completely remove the +1 speed, so even if you used this situation, the final stat would be still be the same as the last situation: 123.
Also, Pokemon such as Entei often use priority moves in competitive. In your case, I'm assuming this Entei chose the move "Extreme Speed," which will outspeed your Pokemon regardless of their speed stat unless they use a move of similar priority. More info on priority here.