Hello Nayara,
I think it's good that you're taking this endeavor seriously, because although Whitney trail is not technical, it by no means is a walk in the park. I think physical conditioning and altitude conditioning is vital. 8 to 13 miles with loaded pack is a good start, but it would be better if it has hills with couple of thousand feet of elevation gain. Or you can train on a stairmaster with loaded pack. Acclimatizing to high altitude is also very important. If you have mountains higher than 10,000' in your area, spending a day up there one to two weeks prior to your Whitney date would help. If not, you may want to arrive at Whitney Portal day or two earlier and camp there, and maybe day hike to Lonepine Lake day before the big hike.
As for the trail, you will still find much snow at the end of June, but if they open 99 switchbacks, you may not need mountaineering skills or gears. Considering that 1000-2000 people will use that trail from now to June 27, I'm hoping the trail is well carved out by then.
Many start their day hike at 1-3AM. If you get to the trail head about that time, You will see other day hikers with their headlamps.
I plan to hike the trail on June 20th, and will post the conditions then.
Good luck!
