After looking at some wall of stone and attack spells I began to wonder: Aside from using technology, is there any way via the use of magical weapons, spells, or his own abilities? How a PC could destroy a stone wall? (5×5 ft) within 2 rounds or 3.
So you want to break down a stone wall, huh? The sidebar on page 515 of the Core Rulebook covers this.
Under most circumstances, you can't.
Let's suppose that your wall is made of hewn stone. The CRB says:
Strong walls, such as well-maintained masonry or hewn stone, can't be broken without dedicated work and proper tools. Getting through such walls requires downtime.
In this sense, it won't be possible to accomplish in a few rounds in any circumstance.
But for real - you need to deal at least 70 damage
An object is destroyed when it reaches 0 HP. Hewn stone walls have a hardness of 14 and 56 HP. That means to destroy it in a single attack you will need to deal 70 damage.
You can deal that damage any way you want. A hypothetical level 10 barbarian1 can make three attacks, each dealing an average of 40 damage. The wall's hardness will reduce each attack to 26 damage. Three successful strikes will deal 78 damage on average, enough to destroy the wall.
Optimization is left as an exercise for the reader.
If you'd like to sidestep doing damage all together, the Disintegrate destroys a targeted object immediately. It's a level 6 arcane spell. It affects at most a 10 foot cube of wall.
1 This hypothetical barbarian has a maul with a striking rune, dealing 2d12 damage on a successful strike. Their 20 strength score adds +5 damage. They are using the giant instinct specialization ability to deal +10 damage. Furious Finish adds +5 and weapon specialization adds +2. Finally, their weapon has two property runes which each add +1d6. Their damage roll is 2d12 + 22 + 2d6. On average, this deals 40 damage.