Magento 1.9 Separate XML sitemap for categories and products

I am maintaining a Magento 1 store from the SEO perspective and I hope for your help. I have been looking for answers inside the forum and elsewhere. But I have found nothing, what describe clear the process.

Question 1:
In Magento 1.9, how can I have one XML sitemap for products, a second sitemap for categories and one sitemap for the remaining pages, like Company and Service?

Question 2: Currently all products and categories are in one sitemap. Where do I set that “Last-Modified” is not renewed every day for pages that I have not worked on? Currently, the Last Modified date is renewed every day for all products and categories. Which is not true.

I hope you can help me.

Thanks a lot for your help.