Can the treatment for blemishes be effective and my skin texture improve at the same time?

Lately, I’ve noticed some light blemishes around my cheeks and nose, but my skin texture isn't smooth either, so I’m concerned about both issues. Even if the pigmentation disappears, if the texture remains the same, I feel like my skin won't look clean overall, so I’m wondering what kind of care I should prioritize.

Is it common to start by treating blemishes to even out skin tone, and then manage skin texture separately?

I am curious whether the effects of treating blemishes focus only on pigmentation, or if there can also be changes in skin tone or texture depending on the treatment method.

I would also like to know if it is possible to receive blemish treatment and other skin procedures on the same day. Rather than doing multiple treatments at once, I would like to proceed step-by-step to minimize stress on my skin, so I am curious if you can help determine priorities during the consultation.