No, but you can hire a butler to bring you certain items. I believe he charges a small fee though.
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Her house is in Draynor Village; it is the only house in Draynor with a cauldron, near the bank to the East.
no you can not sell your house on runescape.
You can not put banks in Player Owned Houses. You can how ever hire a butler, he will fetch certain items from the bank for a small fee.
While on RuneScape PVP worlds, if you die, you only lose the items you are carrying, not those in your bank, never in RuneScape will a death directly affect your banked items.
varrock, above the west bank