I created a list template and added it to another site. If I delete the template will the list I added on the other site also be deleted?
No. If you create a list from a template on a site, and then later delete the template, your list will be unaffected. There is no cascading deletion behavior that will delete your list, so your list is safe.
Yes you can delete the template from list template gallery, it will not impact active libraries. You can refer to below forum post for confirmation:
Libraries created from a template are not tied to the template, so the template can be removed if it is no longer required. The same holds true for Site Templates.
Yes, the template can be removed.
One more thing, if you don't want delete the List template or having some fear than you can hide it from UI. in Template just hide it.
<ListTemplate Hidden="TRUE" />
But is you have the list definition than its different story.
Yes, After create a list from Template, there is no connection between List and Template.