1. if you import a client component into a server component, it stays the same. your client component remains a client component while the other parts of your server component remain the same.

the idea for marking specific parts of your app as client and leaving the rest unmarked is so that you ship the least possible amount of client-side Javascript which helps to improve performance.

for example, in this layout file below, rather than make the whole layout a Client Component, move the interactive logic to a Client Component (e.g. <SearchBar />) and keep your layout as a Server Component. this means you don't have to send all the component Javascript of the layout to the client.

// SearchBar is a Client Component
import SearchBar from './searchbar'
// Logo is a Server Component
import Logo from './logo'
 
// Layout is a Server Component by default
export default function Layout({ children }: { children: React.ReactNode }) {
  return (
    <>
      <nav>
        <Logo />
        <SearchBar />
      </nav>
      <main>{children}</main>
    </>
  )
}

as per the last paragraph, both Client components and Server components are actually SSR (server side rendered). see Dan Abramov's explanation here - https://github.com/reactwg/server-components/discussions/4

2. depends. i've been using Context for most of my global Client state management. if you're more comfortable with Redux, why not. it's not an anti-pattern. there are truly things you'd need global client state management for like user authentication.
but for managing data that comes from your server, with Next 13 you can fetch data directly in your Server components using the fetch api, and you can use a tool like react-query for fetching inside your client components.