http to https questions

I changed all my links from http to https and would like to ask if what I have done is correct. Here are my steps:
1) I changed all internal links to https
2) I changed all links in sitemap.xml to https
3) I asked my host to redirect all links from http to https
4) I added in the https site, so now I have two properties in webmasters tools: http and https. For both I have submitted the https sitemap.

Is everything I have done correct? Should I keep the http site in webmaster tools or delete it and keep only the https?
Should I do anything else?

Thank you!

Does use of Google Analytics affect SEO?

I would like to ask some questions about Google Analytics and SEO:
If I use Google Analytics and my site does not perform well, will it drop in Google search in lower positions and if it has good performance is it rewarded and appears in higher position?
Is there an independent from performance reward for sites that use Google Analytics?

Thank you!