Learn English – Is it possible to say “That building is getting more and more higher.”

That "rule" is a very crude approximation of what actually happens.

For most 2-syllable adjectives, either form (more/most or -er/est) is at least "credible" to most if not all speakers, but for any specific word the relative frequency of one may be slightly or significantly greater.

You can add extra "general principles". For instance, two-syllable adjectives ending with –y and –ow, readily take the –er/–est endings, but those with –le and –er characteristically don't for some speakers.

Finally, there are even a few acceptable 3-syllable forms - unlikeliest and unhappier, for example. The un- prefix seems to favour "special dispensation to buck the basic rule", but with apparently 1330 instances in print for almightiest I think we have to accept that one as "credible". With no discernable "extra principle" - it's just a "one-off" that doesn't seem to conform to any rule or exempting principle.

Bear in mind that for any given pair of native speakers it's quite possible they will disagree on the acceptability of certain -er/-est forms.

In the specific case of handsomer,more handsome, as you'll see from that link, usage has changed dramatically over the past century. The latter, more "generic" form is now actually the most common, but C19 usage was dominated by handsomer. What this shows is that people are gradually moving towards implementing the simple rules more consistently, but it's a slow process. Nevertheless, on average we're becoming more likely to favour more/most, and unlikelier to use forms like that

As this link shows, even though I'm presumably unassailable in having used more common above, a substantial minority would have been perfectly happy with commoner not so long ago.

I don't think the average "learner" really needs to know that some people still find handsomer acceptable (most don't, and you'd never be criticised for saying more handsome, so just do that anyway). I suggest using the more/most forms for all 2-syllable adjectives except where the second syllable ends in /i/ (easy, happy, silly), or the second vowel is a neutral schwa (clever, humble). And I'd call quiet a single-syllable "triphthong", which for me explains why quieter/quietest are okay. But if in doubt, just use more/most.

Both are correct depending on what you want to say. They don't mean exactly the same thing.

"Anything is possible" is very optimistic. One would say this if they were hoping for an extraordinary event to happen. For example, "I would love to learn how to snowboard one day" could be responded with "anything is possible!". In that sense, it's a very hopeful, optimistic phrase.

"Everything is possible" means that every single thing is possible. There is a slight difference between "every" and "any"; every typically means ALL THINGS whereas any means any ONE of those things. If that makes sense. This phrase might stir up some debate because technically speaking, everything is NOT possible. It's not possible for a human to fly without any sort of assistance (as an example). While this phrase has a very similar meaning to "anything is possible", it could very well lead to people giving you retorts as to what is not possible.

I would say that "anything is possible" is far more commonly used than "everything is possible". It also sounds more colloquial for everyday use. I wouldn't blink an eye if someone said "anything is possible", but if they said "everything is possible" that might stir up some debate.