Can i drive alone if i have a under 21 drivers permit at age 18? (in TEXAS) ?

If you're 18 you need to go get your driver's license. If you only have a permit you still have to follow those rules so no, you cannot drive alone.

At age 16, you can finally graduate up to having a provisional license if you have displayed good driving behavior, completed 30 hours of behind-the-wheel instruction, had your permit for at least six months, and passed the driving test. A provisional license will allow you to finally drive by yourself. However, you still can't drive between midnight and 5 a. m., you can't drive with more than one passenger under 21 years old, and you cannot use a cell phone (even with a headset) except in the event of an emergency. These restrictions will be lifted after one year of good driving on your provisional license, or when you turn 18.