I'm making a Fireblood Dwarf, and I'm wondering if I, as a Dragonblooded creature, qualify for taking Dragon feats like Improved Speed and Rapidstrike?
While the fireblood dwarf (Dragon Magic 7) has the subtype dragonblood (DM 4) (and, obviously, dwarf), the fireblood dwarf's type remains humanoid not dragon. Only creatures with the actual dragon type--not just the dragonblood subtype--meet the prerequisites of feats that have as a prerequisite the type dragon, like the feats Improved Speed (Draconomicon 71) and Rapidstrike (73).
Further, were a PC to qualify for such feats because of his type (e.g. when he advances a level the PC is the subject of the spell essence of the dragon [trans] (Races of the Dragon 112-3)) the player must still seek the DM's permission to take the feat if the feat's in the category monstrous (Draconomicon 66).
The dragonblood subtype, however, does allow a creature to take feats that have the dragonblood subtype as a prerequisite, such as some feats presented in Dragon Magic and Races of the Dragon.
RotD (page 4) on the Dragonblood subtype
If a race possesses the dragonblood subtype, it has a strong affinity to dragons—which means that spells, effects, powers, and abilities that affect or target dragons also affect it. The subtype qualifies a creature to use magic items normally only usable by dragons, and qualifies the creature to take feats that have the subtype as a prerequisite. The dragonblood subtype also makes creatures subject to harmful effects that affect dragons.
The dragonblood subtype does not confer the dragon type or any traits associated with that type. For instance, it does not give a creature frightful presence. Dragons automatically qualify for any classes, prestige classes, racial substitution levels, feats, powers, or spells that require the dragonblood subtype. Races presented in this book that have the dragonblood subtype include dragonborn, spellscale, kobold, and draconic creatures. Should a creature acquire the dragon type, it loses the dragonblood subtype.
The problem here is that Dragon is a type and Dragonblood is a subtype, so that sentence refers to being able to take feats with dragonblood prerequisite.
With an arguable conflict:
Humanoid (dragonblood): Dragonborn are humanoids with the dragonblood subtype and any other subtypes they had before undergoing the Rite of Rebirth. For all effects related to race, a dragonborn is considered a dragon and a member of her original race.
Dragonborn defines Humanoid(dragonblood) as being a dragon and whatever they were before for everything. This should probably only apply to those who undergo the rite of rebirth (become dragonborn) however.