If the "cast as _______" then they are for all intents and purposes of spell casting a _______. In the case of the dragon they are a 3rd level sorcerer for all purposes of spellcasting. Which means if there is a wand of a spell on the sorcerer spell list the dragon can use it. For a scroll the dragon must be high enough caster level to be able to have access to those spell slots, so a 3rd level sorcerer has access to any 1st level spells (on their spell list). Otherwise UMD is required.
So a wand can be used as long as the spell is on the class spell list.
Scroll you can use as long as you can cast spells of the same level as the spell on the scroll and its on your spell list.
Othersie UMD is required.
If they have "casts as ___x basically treat them like they are a member of that class.
As far as scrolls read magic or spellcraft works to identify the scroll. Asuming you know what is on it neither is needed to usw the scroll if it is on your spell list.
Using umd for a scroll is a wholly seperate thing.
Activation: To activate a scroll, a spellcaster must read the spell written on it. This involves several steps and conditions.
Decipher the Writing: The writing on a scroll must be deciphered before a character can use it or know exactly what spell it contains. This requires a read magic spell or a successful Spellcraft check (DC 20 + spell level). Deciphering a scroll is a full-round action.
Deciphering a scroll to determine its contents does not activate its magic unless it is a specially prepared cursed scroll. A character can decipher the writing on a scroll in advance so that she can proceed directly to the next step when the time comes to use the scroll.
Activate the Spell: Activating a scroll requires reading the spell from the scroll. The character must be able to see and read the writing on the scroll. Activating a scroll spell requires no material components or focus. (The creator of the scroll provided these when scribing the scroll.) Note that some spells are effective only when cast on an item or items. In such a case, the scroll user must provide the item when activating the spell. Activating a scroll spell is subject to disruption just as casting a normally prepared spell would be. Using a scroll is like casting a spell for purposes of arcane spell failure chance.
To have any chance of activating a scroll spell, the scroll user must meet the following requirements.
The spell must be of the correct type (arcane or divine). Arcane spellcasters (wizards, sorcerers, and bards) can only use scrolls containing arcane spells, and divine spellcasters (clerics, druids, paladins, and rangers) can only use scrolls containing divine spells. (The type of scroll a character creates is also determined by his class.)
The user must have the spell on her class list.
The user must have the requisite ability score.If the user meets all the requirements noted above, and her caster level is at least equal to the spell's caster level, she can automatically activate the spell without a check. If she meets all three requirements but her own caster level is lower than the scroll spell's caster level, then she has to make a caster level check (DC = scroll's caster level + 1) to cast the spell successfully. If she fails, she must make a DC 5 Wisdom check to avoid a mishap (see Scroll Mishaps). A natural roll of 1 always fails, whatever the modifiers. Activating a scroll is a standard action (or the spell's casting time, whichever is longer) and it provokes attacks of opportunity exactly as casting a spell does.
Determine Effect: A spell successfully activated from a scroll works exactly like a spell prepared and cast the normal way. Assume the scroll spell's caster level is always the minimum level required to cast the spell for the character who scribed the scroll, unless the scriber specifically desired otherwise.
The writing for an activated spell disappears from the scroll as the spell is cast.