Questions & Answers about Quiero solicitar un permiso.
After querer when you say you want to do something, the next verb stays in the infinitive.
- Quiero solicitar = I want to apply/request
- Quiero comer = I want to eat
- Quiero hablar = I want to speak
So quiero solicito is incorrect because solicito is a conjugated form, and after quiero you normally need the infinitive: solicitar.
In Spanish, subject pronouns are often omitted because the verb ending already shows who the subject is.
- quiero already means I want
- so yo quiero is possible, but usually unnecessary
You would add yo only for emphasis, contrast, or clarity:
So Quiero solicitar un permiso is completely natural.