[RPG] attack with a weapon and then cast Shocking Grasp in one turn

Firstly, Extra Attack is a class feature, not a feat.

Secondly, Extra Attack says:

Beginning at 5th level, you can attack twice, instead of once, whenever you take the Attack action on your turn.

To cast Fire Bolt, you take the Cast a Spell action, not the Attack action. Extra Attack only applies to the Attack action.

You can cast with any free hand; you don’t need two. So you can cast the spell in one hand and have the dagger in the other. And drawing a weapon is a move action anyway; if you have BAB +1 you can even do it while moving.

You cannot attack with the dagger to discharge shocking grasp however, simply because the rules allow you to discharge it with a touch attack, or with an unarmed strike, and with no other action. There is an ill-regarded and poorly-conceived line about unintentionally discharging the spell by touching anyone or anything. I strongly recommend ignoring it, as it conflicts the rest of the rules, and allows all manner of broken abuses.

As a form of circumstantial evidence, I point to all the variety of options for allowing weapon attacks to discharge spells: they all involve particular investment on your part. They would serve no purpose if you could do it without those investments. For examples, the spellsword class’s Channel Spell feature in Complete Warrior, the duskblade class’s Arcane Channeling as well as the Smiting Spell metamagic feat in Player’s Handbook II, and so on.