I'm creating a level 4 character and I start off with 1 level 3rd, 2 2nd level and 1 level 1 item.
My monk is using unarmed strikes and not wearing any armor.
Can I use these 1st level treasures: a potency crystal, owlbear claw or jade cat onto my fists or unarmed strikes?
So you're making a monk as well huh? Nice.
The answer is yes, as long as you choose the Bracers of Armor 1st and the Expert handwraps of the mighty fists as your 2nd level treasures. Those are the two pieces of gear you'll need to affix the trinkets.
It has this item listed as 'consumable'. How many times can I use this potency crystal? It seems very good unless it's just 1 use item.
It's one-use.
We’ve ratcheted up the wonder of magic items, including reimagining them as truly special belongings and
designing new consumables, called trinkets, as the martial counterpart to scrolls
and
Trinkets
An item with the trinket trait is a magical charm, gem,
stone, or other small object affixed to armor, a shield, or
a weapon (called the affixed item). Each trinket holds a
sliver of combat knowledge or magical energy that can be
unleashed for a momentary boost of power or enhanced
ability. Many trinkets can be activated as a free action
when you use a particular type of action or activity.
You must be wielding or wearing an item to activate a
trinket attached to it. Once activated, a trinket burns out
permanently, usually crumbling into a fine dust.
Can you take this item as a 'permanent' item for wealth by level- 1st level treasure?
You shouldn't use permanent item slots to get consumables. Its a waste. But often there's nothing else better. So, in theory, yes, you can do that.
Dull Grey Aeon Stones are permanent level 1 treasures- they don't do anything except "orbit your head" though.
But really the "level 1 permanent items" is there for:
When assigning level 1 permanent items, your best options are weapons, armor, and gear from Chapter 6 worth between 10 and 20 gp.
Which is to say if you're building a character at a higher level, you just slot your mundane equipment in there without having to worry about the monetary cost. Since monks don't want weapons or armor, get a skill kit or something.
Or heck, ask your group if there's anything they might need and can't find the space for.