Can I raise a hero out of its tier?

I mean you can certainly make a unit that outperforms it's tier, but the ratings are based off of BST and inherent skills, which can't be changed so certainly you can build and merge a unit to something that definitly outperforms it's rank

Tierlist are made from the opinion of the person who creates is, it's just from personal opnion, not from builds from other people, so i don't think they will their tier list just from your build. Also tier list are not to follow word for word, any character in the lowest tier can be made good in some sort of niche, just use what you fell like using.
Alm's case is different becuase he jumped tiers thanks his awesome Falchion refinement

I'm not quite sure, so take it how you will, but first off tiers are completely subjective, and often have to put merging and IVs into consideration. Gerome has an extremely similar stat-line to his mother Cherche, but she has access to IVs and is capable of being merged to +10, something Gerome doesn't have, which explains her higher placement. Another thing is with Alm, he was arguably the worst Falchion user in the game, but when his refine came out, it gave him an extremely busted ability, which is why he is top tier now. Not because someone used him in a different way, but because IS gave him a massive buff.

Every unit can be good with the exception of a few, there is no reason to be so fixated on what a website claims, but just by looking there are units that are definitively better than others especially when they perform the same role. That essentially determines the tier. Gerome is not a bad unit running Brave Axe, but performing the same role, there exist better flier axe users that utilize the same build better, like Cherche. What made Alm increase in tier is the update to the Falchion. Alm from a mediocre Falchion user with middling speed now has a Brave Sword effect. With this in mind, it doesn't matter what build a unit has.

Tier lists aren't something that people should be worrying about since, a lot of the time, they are just opinionated. Speaking of which, so are builds. On build pages, the "optimal" build is not something everyone finds to be.. well, optimal. I think Lucina's most optimal build is with Distant Counter, and I disagree. Yes, it works, but, in my opinion, it's not optimal.

Alm increased in tiers after his Falchion was refined if I recall (at least people kept saying this was the case), so... yeah.

Alm moved up because his Falchion received a new buff that makes it far more competitive. So universally its a better unit. Your builds here wont influence the tier system if that is what you are asking. Tier list is simply what a handful of experts rate a unit.

Sure, with the proper dedication your unit can reach the listed tier of that unit if not exceed it.

Smogon, now that's the good stuff. B)

Anyways, I don't think it can really be raised out of a tier, since I'm pretty sure the tiers are just raised off BST and stats in comparison to other units. For example, a Cherche could probably be built the same as that Gerome you make, and it'd probably do the job better thanks to higher merge potential. You can make an insane build (and I'd love to hear about it!), but it's pretty concrete rankings, generally.

Mamoswine to the top

I think the units are ranked on their BST first, then starting kit (specials/supports/ABC slots). Any unit can be good with inheritance skills. For example Brave Lynn. Her starting kit is basically perfect, and you don't HAVE to replace anything. But if you decide to give her a brave bow she's pretty much god tier