I believe Sevilla's
Feria de abril begins on 12 Apr this year (early Easter). It's worth a stop.
As to seeing Northern & Southern Spain in 2-weeks, that will be a problem unless you fly to intermediate destinations. Vueling, Spain's new discount air carrier (operating out of Barcelona) has some excellent fares/schedules. Iberia and Spanair both have 'Visit Spain' plans: so much per flight segment with a minimum purchase of 3-segments.
I was in Potes (Cantabria) for Santo Toribio (16 Apr) one April not to long ago: Search & Rescue
Guardias, who rescue people in the mountains, were having a competition that included cross-country skiing. That might give you an idea of what to expect in the north.
For a first time visitor to Spain: In April, unless you have compelling reasons for visiting northern Spain I think I would limit myself to the south.