From Player’s Handbook page 171:
COMBINING MAGICAL EFFECTS
This broad category begins with the primary rule of the section.
Spells or magical effects usually work as described, no matter how many other spells or magical effects happen to be operating in the same area or on the same recipient. Except in special cases, a spell does not affect the way another spell operates. Whenever a spell has a specific effect on other spells, the spell description explains that effect. Several other general rules apply when spells or magical effects operate in the same place:
So, as a baseline, everything stacks except for the exeptions it defines. The list of exceptions, in addition to special cases listed in the actual spell descriptions, includes these topics:
Stacking Effects: This section begins by explicitly defines what stacked effects it refers to:
Spells that provide bonuses or penalties on attack rolls, damage rolls, saving throws, and other attributes usually do not stack with themselves.
It then goes on to describe italicized sub-categories of “Stacking Effects” which all fall under the initial umbrella defined in the first sentence of the category section. I.e. “Same Effect More than Once in Different Strengths” is a sub-category of “Stacking Effects,” so this sub-category applies only to spells affected by the “Stacking Effects” rules.
Spells with Opposite Effects: This section does not limit application of effects, but simply describes in what order to resolve them excepting for spells with built-in special-case interactions.
Spells with opposite effects apply normally, with all bonuses, penalties, or changes accruing in the order that they apply. Some spells negate or counter each other. This is a special effect that is noted in a spell’s description.
Instantaneous Effects: This section removes instantaneous effects from the rules set forth in “Stacking Effects”
Two or more spells with instantaneous durations work cumulatively when they affect the same target.
Unfortunately, the “Instantaneous Effects” section includes an example of a damage spell. This adds a lot of confusion, because without this example, there is no question about damage being limited or not.
For example, when two fireballs strike a same creature, the target must attempt a saving throw against each fireball and takes damage from each according to the saving throws’ results. If a creature receives two cure light wounds spells in a single round, both work normally.
Note that an example does not create rules. The rules have not explicitly defined damage as an exception to the primary rule set forth in the “COMBINING MAGICAL EFFECTS” section that clearly states things work as described no matter what except for the defined special cases.
ANSWER 1 of 2: Yes, power word: pain stacks because damage is not restricted from stacking per the PHB rules.
ANSWER 2 of 2 (edit: corrected): Yes, casting cause fear twice will fear an opponent.
I re-read the rules for combining magical effects, this section in particular:
Same Effect with Differing Results
The same spell can sometimes produce varying effects if applied to the same recipient more than once. Usually the last spell in the series trumps the others. None of the previous spells are actually removed or dispelled, but their effects become irrelevant while the final spell in the series lasts.
I had originally answered that the effects will not work because a spell with the same name that causes a bonus or penalty (which the effect frightened, granted by cause fear, does) cannot stack with itself as a basic rule. However, there is an exception carved out that I somehow missed in my previous reading, quoted above, which states that multiple such castings of a spell can work if subsequent applications “produce varying effects,” and multiple applications of frightened produces a varying effect as a matter of course.