How many artifacts are there, do they have any effect?

Post-game edit: Just finished the game and I can conclude that the starting/subsequent artifacts have no effect on your game whatsover. Also, it is possible to finish the game with a level one character (I just did).

I have no idea what the starting banner's effect on the gameplay is, but it's on every character you start with. It's called the 'Ashes of Life', and story-wise, in King Boldof's request, he mentions

Collect the four artifacts that slumber in our kingdom.
When those artifacts and our heirloom, the Ashes of Life, comes together...
Peace will rule on Earth.

The other four slots are for your artifacts. You can get more artifacts by defeating the dragon every 10 floors.　　　　　

1ビットローグは、10フロア毎に強敵「ドラゴン」が登場します。ドラゴンを倒す事ができると、やり込み要素「アーティファクト」を入手する事ができます。

When you defeat a dragon, you get a random +1 to your attack or durability.

10, 20, 30, 40, 50回で出現するドラゴンを倒すと、攻撃力(ATK)または武器耐久度(DCY)が上昇します

The reset button is translated from "Give up" in Japanese, so if you press that (and the confirmation button), you'll be returned to the main menu with your gold / levels intact. It's probably better to give up than to die to an enemy, I guess.

Source: Me. Downloaded the game and trying it out in Japanese now.