Hi there, johnboy412000! Thanks for playing the trial.
As I've stated before, this design of this game is based on the old Nintendo RPGs of the early 90s. These games were somewhat less forgiving than RPGs are today. It is not uncommon in a classic Final Fantasy game (FF3 being the prime example) to die in the intro due to bad luck or bad strategy -- and of course you can't buy potions in an intro area. Final Fantasy VI didn't let you shop during the intro dungeon. Nor did Final Fantasy VII, for example.
The difficulty of this game is not for everyone, but it is designed so that you have to make full use of the abilities available to you to make it through the battles. You should be making full use of Lionel's First Aid skill -- this can heal your HP right back up to full. You have Salves and Peptides in your inventory which can also restore your HP and SP. Make use of Lionel's Double Strike skill to deal extra damage, and Felix's Toxic Curse skill to weaken the enemies. You can also have Felix use Speed Up so he gets extra turns, which allow him to deal more damage.
Use the Turn Guage in the top left corner of the screen to see when the enemy's turn is coming up, and prepare for it. If your HP is low, use the turns right before the enemy's attack to heal up and Block to reduce the incoming damage. Getting through the intro area without losing a character is quite possible as long as you're actually thinking about your actions during the fights.
After you complete the intro area (which really shouldn't be more than the first 20 minutes of the game), you'll get to go to the world map, visit towns, buy stuff etc. It's basically just like an old-school RPG in that regard. There's a linear intro area to establish the story and familiarise you with the game mechanics, and then you get into the game proper.
Happy adventuring!