Whenever I see ASOIAF discussed in a meta sense, it always seems to be regarded as a deconstruction, and subsequent reconstruction to some, of a fairly abstract “standard fantasy”. I’ve got relatively little exposure to non-dark fantasy, so while I’ve got an idea of the tropes and/or cliches at work I haven’t seen them in action too much. Can you recommend a few that would help give insight into “standard fantasy” in action?

Well, there’s always been multiple variants of fantasy, which you can array on a spectrum from High Fantasy to Heroic Fantasy to Sword & Sorcery to Low Fantasy. When people talk about standard fantasy, they’re usually talking about either High or Heroic, and they’re usually talking about your Standard Fantasy Setting in some vaguely Medieval European direction.

Hopefully those TV Tropes pages should give you some examples, but you won’t go far wrong if you read a cross-section of Tolkien, Dungeons & Dragons novels, David Eddings, and Terry Brooks.

How should be a fantasy set in the renaissance ?

Great question!

I’ve actually been thinking about this a couple years before I started getting into ASOIAF.

Here are some things I think Renaissance fantasy should emphasize to set itself apart from High Fantasy or medieval fantasy:

Different geographies: High Fantasy/Medieval fantasy tend to be set either in rural countrysides (following the pastoral tradition) or vast, untamed wilderness (following the Romantic), largely due to Tolkein’s anti-modernism. The Renaissance very much was an era in which cities and commerce and finance were starting to become important, rather than just subsistence agriculture.
Different societies:
High Fantasy/Medieval fantasy hasn’t traditionally interrogated class particularly well, and so you tend to get idealized images of happy peasants, rightful kings, and brave knights. (It’s only in recent years with the rise of deconstructionist fantasy that we’ve started to question this stuff.) But in the Renaissance, you start to see merchant families and guilds not just exerting political influence, but outright running city-states.
Different politics: rather than just kings and lords, “you’ve got various forms of Republics, mercantile city-states, and petty princedoms, all of which gives much more scope for ordinary people to do important things.”
Different cultures: rather than an emphasis on the ancient and the eternal, there should be an emphasis on cultural change. “an explosion of knowledge, with a bubbling ferment of science, arts, literature, philosophy, history, political science, and a roster of geniuses whose human brilliance is much more appealing than the aloof [I think I was leaning towards alien or inhuman, without really putting my finger on it] other-ness of a Merlin.”
Cosmopolitanism: in part because of urbanism and in part because of increased trade, you have a lot more cultural diversity, so in my mind Renaissance Fantasy ought to involve a melange between many different cultures beyond Expies of white Europeans, with cities full of immigrant workers, foreign merchants and diplomats, imported goods and ideas, a sense that the city is part of a global network.

Hopefully, Renaissance fantasy should help us move beyond repetitions of the Return of the True King by way of the Hero’s Journey, and allow us to tell other kinds of stories.

How common we’re war hammers and axes in the Middle Ages? I feel they’re over represented in fantasy

Answered here.

Warhammers and axes weren’t uncommon, especially during the Late Middle Ages once armor got good enough that you couldn’t easily cut through it with a sword. In that situation, a warhammer or axe were really good at concentrating force to a point, hopefully smashing through their armor, but if not definitely knocking them down so that you could put one of these through a weak point:

That’s not to say that people stopped using swords – there’s a whole bunch of rather clever folks who’ve gone back to arming manuals to rediscover how people used half-swording and other techniques to deal with opponents in plate – but those techniques were rather advanced and involved. It’s a lot simpler and easier to grab an axe or a hammer and smack someone in the head until they fall down.