Language Switch with HUGO

I'm creating a multilingual Website with HUGO and I wanted to implement a language switcher via HUGO shortcodes. I've run into two problems, each with different code input. But it is all about the language switcher.

Problem 1: When i use this part of code. I'm getting this error:

execute of template failed at <.Page.Permalink>: can’t evaluate field Page in type *langs.Language

<ul>
    {{ range .Site.Languages }}
        <li>
            <a href="{{ .Page.Permalink | relLangURL .Lang }}">{{ .LanguageName }}</a>
        </li>
    {{ end }}
</ul>

Problem 2: When I use this part of code. I'm getting a problem with switching back to the previous language. The link goes from example.com/en to example.com/en/de. And obviously this won't work.

<ul>
    {{ range .Site.Languages }}
        <li>
            <a href="{{ .Lang | relLangURL }}">{{ .LanguageName }}</a>
        </li>
    {{ end }}
</ul>

My hugo.toml is setup like this:

defaultContentLanguage = "de"
defaultContentLanguageInSubdir = true

[languages]

 [languages.de]
  title = "New Page"
  languageName = "Deutsch"
  languageCode = "de"
  weight = 1
  contentDir = "content/de"

  [languages.de.menu]

   [[languages.de.menu.main]]
    identifier = "home"
    name = "Home"
    url = "/"
    weight = 1

   [[languages.de.menu.main]]
    identifier = "about"
    name = "Über mich"
    url = "/about/"
    weight = 2

 [languages.en]
  title = "New Page"
  languageName = "English"
  languageCode = "en"
  weight = 2
  contentDir = "content/en"
  
  [languages.en.menu]

   [[languages.en.menu.main]]
    identifier = "home"
    name = "Home"
    url = "/"
    weight = 1

   [[languages.en.menu.main]]
    identifier = "about"
    name = "About Me"
    url = "/about/"
    weight = 2

What am I missing out? Did I use something deprecated (Hugo version v0.127.0)?

Problem 1

Classic context problem: The field.Page does not exist in {{ range .Site.Languages }}. The correct way to refer to it is by using $.Page, where the dollar sign refers to the previous context.

Problem 2

This will be solved when you solve problem 1.

Here is the working code:

<ul>
    {{ range .Site.Languages }}
        <li>
            <a href="{{ $.Page.Permalink | relLangURL .Lang }}">{{ .LanguageName }}</a>
        </li>
    {{ end }}
</ul>