When you use draw_set_alpha(), as well as other draw_set_.. methods, you change global settings for drawing everything after it across the entire project.
Take as a rule, revert such settings back, after you draw the needed thing. So, according to your code above, you should use this:
//Object 1: (draw event)
var prev_alpha = draw_get_alpha(); //getting current alpha settings
draw_set_alpha(0.5); // setting needed alpha
draw_text(x,y, global.Score); //drawing text with 0.5 alpha
draw_set_alpha(prev_alpha); // setting alpha setting back
// the same for the second object
//Object 2: (draw_event)
var prev_alpha = draw_get_alpha();
draw_set_alpha(1);
draw_text(x,y, global.highscore);
draw_set_alpha(prev_alpha);