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Anyone who has at least one rank in UMD can attempt to use it to activate these items.
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I'll cover wands first because they are easy.
If you have the spell on your spell list you do not get(need) to make a UMD check to activate a wand. It simply works.
If you do not have the spell on your spell list the DC of the UMD check is 20 to activate the wand.
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Scrolls get a bit more complicated. In order to activate a scroll you need:
1 To be the right type of caster (Arcane, Divine or Psychic)
2 Have the spell on your spell list
3 Have a high enough ability score in the required casting stat. (10+spell level)
For example you need a wisdom of at least an 11 to activate a scroll of a 1st level cleric spell.
If you meet all of these requirements and your caster level is at least equal to the caster level of the scroll then you need no check.
If you caster level is less than the caster level of the scroll then you need to make a Caster level check. The DC of the caster level is the scrolls caster level +1.
For example a 1st level cleric trying to cast a scroll of hold person would need to take his caster level (1) and roll a d20. The number he needs to reach is 4 assuming the scroll was made at its minimum caster level. Hold person is a second level spell for clerics so can be cast by level 3 clerics. 3+1= 4.
If you do not meet the above requirements you can get around them with use magic device checks.
You can emulate a higher ability score with UMD. Your ability score is treated as the result of your UMD check -15. In order to use that scroll of hold person you normally need at least a 12 wisdom. If you do not have that 12 wisdom a UMD check of 27 will suffice.
If you do not have the spell on your spell list you can use UMD to pretend that you do. The DC of this check is 20 + spell level.
For example your rogue wants to use a scroll of magic missile made by a first level wizard.
The rogue does not have magic missile on a spell list.
First thing you need to do is make a UMD check of 21 (20+spell level).
Then you need to check to se if your intelligence is high enough. Magic missile is a first level spell wich requires at least an 11 in the appropriate ability score. (10+spell level, Int because it was made by a wizard) (technically you could instead emulate a sorcerer and use charisma instead, let's say you don't have that either).
You need to make a UMD check to pretend to have that high of an ability score. The DC of this check would be 26 (15+ability score needed).
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Your race is mostly irrelevant (unless you are activating an item that depends on race)
1) yes, anyone can use UMD (DC20) to use wands, unless it is a ranger spell, in which case your character does not need a UMD check at all (unless you are playing a spell-less variant) because you have a spell list even at level 1 when you can't cast spells yet.
2) Scrolls are a little more complicated, as you need to decipher it and you may need to emulate an ability score requirement as well. it's a 3 step path.
a) decipher the scroll, which you can do in advance (DC25+spell level)
b) if you don't meet the minimum ability score requirement* emulate an ability score (DC10+the ability score you require)
c) cast from the scroll (DC20+spell level)
if it is a scroll of a ranger spell, you just need to decipher the spell and maybe make a caster level check if your level isn't high enough.
*you need a minimum ability score (int for wizard spells, wis for cleric spells) to cast spells of 10+spell level.
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To make it super simple for your Ranger/Rogue/Fighter:
For Wands
Is the spell a divine spell on your spell list?
If yes: then no check needed. You are able to activate it.
If no: DC 20 UMD check needed.
For scroll
Step A) Is the spell a divine spell on you spell list?
If yes: go to step B.
If no: make a UMD check DC = 20 + spell level. If you succeed go to step C.
Step B)
Is your caste level high enough? (Your caster level is the number of levels you have in the class you are using, this case Ranger).
If yes: Go to Step C.
If no: make a caster level check (caster level+ d20). The DC is the caster level of the scroll + 1.
Step C)
Do you have a high enough ability score (the ability used in casting for the class you are emulating/using)? (10+spell level)
If yes: congrats the spell works!
If no: make a UMD check. The DC is 15 + the number you need in that ability.
If you fail any of these checks:
The scroll does not activate.
If you failed the caster level check, make a DC 5 wisdom check or you suffer a mishap. A natural one one this wisdom check always results in a mishap.
What the mishap is is up to your DM.
Here is a list of possiblities.
A surge of uncontrolled magical energy deals 1d6 points of damage per spell level to the scroll user.
Spell strikes the scroll user or an ally instead of the intended target, or a random target nearby if the scroll user was the intended recipient.
Spell takes effect at some random location within spell range.
Spell's effect on the target is contrary to the spell's normal effect.
The scroll user suffers some minor but bizarre effect related to the spell in some way. Most such effects should last only as long as the original spell's duration, or 2d10 minutes for instantaneous spells.
Some innocuous item or items appear in the spell's area.
Spell has delayed effect. Sometime within the next 1d12 hours, the spell activates. If the scroll user was the intended recipient, the spell takes effect normally. If the user was not the intended recipient, the spell goes off in the general direction of the original recipient or target, up to the spell's maximum range, if the target has moved away.
It is also important to note that in PFS all wands and scrolls are considered both arcane and divine if both types of casters have the spell on their spell lists. For example resist energy scrolls are treated as both arcane and divine because it is on both the cleric and the wizard/sorcerer list. PFS does this for simplicity.