I’ll begin by addressing the bullet points directly, but I think you are somewhat misinformed about how magic items work in general, so I recommend reading the rest of the answer as it tries to explain things in a bit more detail.
- If the DM makes up a wondrous item or weapon, how does he determine the caster level?
For these sorts of items, the caster level is just made up as long as it’s high enough to craft the item. Wizards of the Coast does not appear to have given it very much thought, so you probably don’t need to worry about it either.
- If an item has two 2nd level spells on it, does that increase the caster level, or just the gold value?
Depends what you mean by having a spell “on” the item—if you mean requiring the spell to craft the item, then having a second spell changes nothing unless it’s a higher level spell. If it is a higher level spell, then the minimum caster level to craft the item increases, but this doesn’t affect the cost.
If you mean that the item can cast both of these spells, then you have pay 50% extra for the lower-level spell, so that increases the cost. Again, if the second spell is higher level than the first, then this will also increase the caster level, and in these situations, the cost goes up (a lot).
- Can two items that are otherwise identical have different caster levels (resulting in one being more powerful because of longer range, duration, etc.)?
Yes, but for most items it doesn’t change anything except to make the item somewhat less susceptible to dispel magic. For items that actually cast spells, the higher caster level does increase the range, duration, and other variables of the spell that is cast.
All that said, I think you need a bit more information on how magic items work, and about the format that magic item descriptions use (it’s kind of misleading).
First, I think it would help you to think about two separate classes of item: those that cast some spell, and those that perform some other magical effect, usually in a continuous or permanent way. Those items that cast a particular spell have detailed rules about how different combinations of spells work, how caster level affects the item and the spell it casts, and how much all that costs. Those items that don’t cast a spell, on the other hand, just have some fixed effect that usually doesn’t really change, in effect or in price, based on caster level. You’ll want to keep these two types of items separate in your head.
Now then, as to the magic item descriptions that you’re reading: the caster level listed for magical items is there for the DM’s convenience only. This is the caster level that the item in question is generally found at, when it’s found as part of loot or available for sale and the DM doesn’t want to think too much about who made it.
These caster levels are generally pretty arbitrary, just made up by the item’s author. They are not a requirement for crafting the item.
When a PC, or NPC for that matter, creates an item, its caster level is set by the crafter to somewhere between the minimum for the item, and the caster level of the crafter him-or-herself.
For spell-mimicking items, as discussed above, caster level is important. It’s also very expensive. As a result, most crafters strive to create these items at the lowest caster level possible. Spells that really need higher caster level are often avoided for these items because of the expense.
For most armor, weapons, and wondrous items, the ones that don’t cast spells, caster level doesn’t do very much, but it’s also free. So the crafter will usually use the highest caster level he or she can.
The minimum caster level here is usually the one you need to cast all the spells involved in the item. So if an item requires fireball in its creation, the minimum caster level is whatever the crafter needs to cast fireball—5th for wizards, 6th for sorcerers. If the item lists “CL 10th” in its description, ignore it: CL 5th or CL 6th versions of this item are possible, and cost the same unless this item is going to actually be casting fireball.
A few items however, do explicitly require a certain caster level to get a certain bonus. These are especially the ones where you can buy higher bonuses for the item (magic weapons and armor, cloaks of resistance, ability score enhancement items, and so on), so even though this exception only applies to a few items, they’re some really important ones. This requirement is explicitly listed in the crafting requirements, and isn’t necessarily the same as the caster level listed for the item. For example, from cloak of resistance’s requirements section:
Craft Wondrous Item, resistance, creator’s caster level must be at least three times the cloak’s bonus
This requirement has nothing to do with the CL 5th stated in the previous section; that is just the typical caster level of a cloak of resistance. A cloak of resistance +1 is craftable at caster level 3rd, while higher-caster-level cloaks are possible, making them harder to dispel (and not costing any more unless you also increase the bonus).
In general, the usual caster level thing is more confusing than it is helpful, in my opinion, and the chosen numbers often make no sense:
CL 5th isn’t even high enough to be allowed for a cloak of resistance with a resistance bonus higher than +1.
Sovereign glue is a very cheap magical item—that is stated to typically have caster level 20th. To have caster level 20th, it would need to be crafted by a 20th-level spellcaster: why on earth would such a powerful character spend his time creating such a minor and cheap item?
So as a DM, when creating these kinds of items, feel free to just make something up and not give it a second thought: that’s all Wizards apparently did in the first place, after all.
For items that actually cast spells, caster level can matter a lot more, and has a lot of effect on the item’s value, so give those a lot more thought. The Creating Magic Items rules have detailed descriptions of how these kinds of items are created and priced.