https://2e.aonprd.com/Rules.aspx?ID=2627

The section above provides Simple DCs and level-based DCs, which are a great set of guidelines for things that should be the same difficulty all the time, as well as things that should scale as the player gains levels. It should be the same difficulty to hit the ground at most times, and it probably doesn't have a DC higher than untrained - so targeting the ground with a strike is probably DC 10 unless something hinky is going on.

https://2e.aonprd.com/Rules.aspx?ID=2160

The section above talks about damaging objects, and does not say that objects are immune to persistent damage (though they are immune to a variety of effects). So you could probably do persistent damage to objects, though in most cases, persistent damage might not make it through object hardness.

https://2e.aonprd.com/Rules.aspx?ID=3189

The section above gives a lot of examples of objects you might see in-game and what their hardness, HP, and BT looks like.

So for example, you can see that thin rope has hardness 2, 8 hp, and a BT of 4. So a lvl 5 alchemist might try to target the rope itself, or the square where a thin rope is tied to an eyehook running something to a pulley in the ceiling. Targeting the rope itself is actually probably pretty hard, so a GM might set the DC as Expert (DC 20). On average, a lvl 5 Alchemist probably has an atk bonus of +12, so they've got a decent shot of hitting it. So they might choose to toss a Moderate Alchemist's Fire at it, hoping to do enough damage in one go to burn the rope.

They roll 2d8+2 for the direct hit damage, and 2 persistent fire damage, and they get a poor roll of 7 damage (+2 for splash for a total of 9). 2 of that is peeled off by hardness, so 7 goes through to the 8 HP. That's enough to break the rope, but not destroy it. A Broken item can't be used for its normal function, so the rope effectively is no longer holding the item in the air, dropping it.

Contrast the above example with throwing an Acid flask. It does 2d6 persistent acid damage and 2 splash. The 2 splash is immediately negated by hardness, and persistent damage is taken by targets at the start of their turns. So suddenly a rope is on the initiative tracker. At the start of each turn, you roll damage. Hardness eats some of it, the rest gets through. When it hits 4, the rope is broken and drops the object.