Quite a few questions packed in there...
Many reasons why they're more expensive, and most of them have to do with audiophile marketing nonsense than anything else. The most expensive part of a tube amp is the iron (power and output transformers). Some rare NOS tubes that the audionut community has fetishized has created demand and driven their prices to astronomically ridiculous levels. However you slice it, tubes will never again come close to the watt/$ that ss will bring, or compete with ss when it comes to accurate reproduction.
'Warmer' is typically a reference to frequency response aberrations. Tube amplifiers generally have high output impedance, which means that there will be frequency aberrations corresponding to the load impedance. The effect is subtle but can add warmth, and often a bit of twinkle up at higher frequencies, corresponding to rises in the speaker's impedance.
But wait, there's more! Tube amps are also often characterized by relatively high amounts of low order harmonic distortion, which has ramifications for tonal coloration. Second order harmonics are exactly an octave above the fundamental, thus consonant, and largely masked, but they can add fullness. Third order harmonics on their own tend to lend a dissonant, covered, nasal sound. Strong second combined with a strong third, as many tube amps produce, tends to open up the covered effect and give a more brassy, open horn like character.
And there's even more! When overdriven, tube amps don't hard clip like a transistor amp, and can be run into the red before becoming audibly objectionable.
Can't in good conscience recommend any commercial tube amps. They're all generally a rip off. I recommend DIY if you're down for it, or a used amp of known pedigree that will hold it's value so you can sell it for what you paid, after you've scratched the tube itch.
It would equal 100 watts. Watts are watts. And that would be a large and expensive tube amp!
I think your question does go back to what I said about being able to run tube amps into overdrive conditions, so let's look closer at that. As the amp is pushed to and past it's limits, more than just the second or third harmonic get excited. Provided the amp is not pushed so far into over-driven conditions to excite harmonics higher than the tenth or so, and it only occurs on transients, that higher order harmonic content is perceived as added loudness. Meanwhile, the amp's actual peak power is no longer increasing, but average levels are. Add all that up and it's basically acting like a compressor. That's where the tube-watts-are-more-powerful myth comes from. And grossly clipped tube amps still sound terrible (or wonderful, if you're using them for your guitar tone).
They may or may not have "lots of headroom" depending on the overall design, and each tube has limits to what it can do in a particular circuit. For example, a 300B in a single ended type circuit will maybe squeeze out 7 watts or so, where a pair of such tubes in a pp amp could achieve considerably more. How robust or saggy the supplies are comes into play as well. And again, it could also concern that ear-friendly clipping/compression behavior giving the impression of more headroom.
Yes. Audible differences typically correspond to how badly behaved the amp in question is. SET amps, for example, are really badly behaved in pretty much all metrics, and it takes something that bad to produce audible differences. I'm hard pressed to differentiate better performing tube amps from unclipped ss power. Limited experience and all the qualifiers, of course, but I have subjected myself to carefully level matched comparisons.
The reality is that tube amps are inferior to ss for music reproduction.
Don't break the bank. Don't even break out your wallet, keep it in your pocket.