I just started learning tapping and have a couple questions:

First, I have the fingernails on my right picking hand longer than my left, because I sometimes finger pick. Not as long as, say, a professional would, but enough so that it feels unsettling to tap with it, compared to a hammer on with a finger from my other hand, where the nails are closely trimmed. Is this a common experience, just something you adapt to? Do people who use tapping cut the nails on their picking hand closer, at least for the finger(s) they tap with?

Second, I was looking at a guitar solo that had a minor chord arpeggio played on one string with a combination of hammering and tapping, such as a D minor on the B string:

h t

I was doing that okay, but then I realized if I wanted to do the same hammer-tap arpeggio with a major chord instead of a minor chord, I'd have to span an extra fret with my pinky hammer, like a D major hammer-tapped like this:

h t

I can stretch my pinky an extra fret while playing most of the time, but I cannot see myself hammering down with that stretch with enough strength to make the note sound good. I guess this is more of a hammer question than a tapping question, but is this a skill most experienced guitarists develop? Or is it not common to hammer-tap major chords on one string? Or, if you do this, do you plan it out so you are doing it higher on the neck (where the frets are closer together). This would surely be doable on the D string, for example:

h t

So I guess the question is whether I should work on being able to hammer a major third gap low on the fretboard, whether for use in arpeggiating a major chord using tapping, or for any other purpose, or whether most guitarists just would figure out a "work around" for this situation, like moving to another string.

The major third interval can be correctly hammered-on by angling your hand such that your index finger on D is curled back and your pinky playing F# is stretched forward.

When you're tapping you should employ a compressor or at least a lot of gain in order to make all the notes sound loudly and evenly.

Each string has a different sound. I personally prefer the sound of the b-string around that range.
Hey dude, I just tried it on my guitar and noticed I found it more natural to use my ring finger instead of my pinky to tap that particular interval. Usually I would use my pinky when tapping major 3rds. To each his own!
yup, I experienced the same thing. I played metal for a decade then got in to classical, so I grew my nails out in my picking hand.

It was weird at first, but I learned over time that I needed to slightly angle my tapping finger different. My middle finger was just slightly extended just a little bit more, so the nail didn't come in contact with the string. It took me a while but I was able to get the hang of it.

as far as the hammer on with the pinky is concerned, don't avoid using the pinkey, it is strong enough to get a good sound. It just may need a little more work right now.

you may want to try this. Any time you do a five fret stretch, you have to have two fingers that have a fret in the middle of them, like your first finger is on the third fret, second is lined up with the fourth fret, third finger is lined up with the fifth fret, and the pinkey has to stretch to the seventh fret.

this means that there is an extra fret between your third and fourth finger. Is this how you are doing that stretch?

if so, try putting that extra fret between the first and second finger (it's the same stretch as making a peace sign). This way the stretch is with fingers that are more dominant, and it wont feel like the pinkey is doing all the work

Hope this helps
on the stretching: it depends on how far along you are as a player. obviously our hands have physical limits, but if, for example, you've only been playing for two years, or you're self-taught, you might not be stretching as far as you physically can. with more experience, you will know how to better apply your hand strength to get closer to your personal, physical limit, yet still play clearly.

being comfortable with proper fretting-hand thumb positioning behind the neck will help immensely with this, so keep that in mind if you aren't already.