Translation:Please go up the stairs.
It's technically grammatically incorrect to use "kudasai" in kanji in combination with a verb. Now that I've learned that rule I like to point it out for others who are interested in the correct usage, but many Japanese people would use the kanji in this situation, you're right.
I think you've picked up on something interesting about the verb 下さる. You can say that a person from above is looking down on someone below, which is why that kanji is used. 上って下さい makes an interesting mental picture when you see the kanji.
And it shouldn't be accepted. を indicates a direct object. "Please go upstairs" would be something like "upstairsに行ってください", whatever the Japanese equivalent of "upstairs" is.
In Duo's sentence, you're performing an action on the stairs by climbing them. In your sentence, you're performing an action by going to a place. Do you see the difference?
You could say that, but it sounds to me like you might be down low using your hands as well to pull yourself up. More common would be "climb the stairs," though that still has the connotation that it is difficult (for example, "we just climbed 10 flights of stairs, and we're exhausted!"). Saying "go up the stairs" is probably the most neutral. You could also say "use the stairs," which doesn't specify up or down.
I'm just speaking for how I perceive those words, though I don't think my assertions are too controversial.