Making a form entry for listserv signup

Hello,
I administrate a website that is run on a multisite platform: http://german.berkeley.edu/. Because I only administrate one site of many, I have access to nothing but the site’s child theme and the WordPress dashboard. I am using the Weaver II theme.

I am trying to create an entry form for a newsletter signup for the homepage, and am trying to put it in the Lower/Left Sidebar in a Text widget. We are trying to achieve something just like the eNewsletter Sign Up at the bottom of this site: http://townsendcenter.berkeley.edu/ .

I can’t seem to get it to work.

Our tech support have provided the following as the code I should be using to create the form:

<form method="post" action="http://example.org/mailman/subscribe/XYZ">
  Your E-mail address: <input name="email"> Your Name (optional):
  <input name="fullname">

  <p>You may enter a privacy password below. This provides only
  mild security, but should prevent others from messing with your
  subscription. <strong>Do not use a valuable password</strong> as
  it will occasionally be emailed back to you in cleartext. If you
  choose not to enter a password, one will be automatically
  generated for you, and it will be sent to you once you've
  confirmed your subscription. You can always request a mail-back
  of your password when you edit your personal options.</p>

  <p>Password choice: <input type="password" name="pw"> Confirm
  Password: <input type="password" name="pw-conf"></p>

  <p>Would you like to receive list mail batched in a daily digest?
  (You may choose NoMail after you join.) <input type="radio" name=
  "digest" value="0" checked> No <input type="radio" name="digest"
  value="1"> Yes</p>

  <p><input type="submit" name="email-button" value=
  "Subscribe"></p>
  </form>

(Original is here: http://wiki.list.org/pages/viewpage.action?pageId=4030596; only thing is that we don’t use mailman for our listserv, we use an institutional version of gmail.)

So I used that, filling in XYZ with the name of the list (german.events@lists.berkeley.edu) and adjusting the action= URL with another link I was provided by tech support: https://calmail.berkeley.edu/manage/list/listinfo/german.events@lists.berkeley.edu

So then it looks like this:

<form method="post" action="https://calmail.berkeley.edu/manage/list/listinfo/german.events@lists.berkeley.edu">
  Your E-mail address:  Your Name (optional): <input name="fullname">  

  <p>You may enter a privacy password below. This provides only
  mild security, but should prevent others from messing with your
  subscription. <strong>Do not use a valuable password</strong> as
  it will occasionally be emailed back to you in cleartext. If you
  choose not to enter a password, one will be automatically
  generated for you, and it will be sent to you once you've
  confirmed your subscription. You can always request a mail-back
  of your password when you edit your personal options.</p>

  <p>Password choice:  Confirm
  Password: </p>

  <p>Would you like to receive list mail batched in a daily digest?
  (You may choose NoMail after you join.)  No  Yes</p>

  <p></p>
  </form>

And the widget automatically deletes the <input name="fullname"> after <form method="post" action="http://example.org/mailman/subscribe/XYZ"> Your E-mail address: <input name="email"> Your Name (optional): every time I insert it.

When I put that into the text widget, I get a block of text beneath our social media icons that reads,

Join the department mailing list!
Your E-mail address: Your Name (optional):
You may enter a privacy password below. This provides only mild security, but should prevent others from messing with your subscription. Do not use a valuable password as it will occasionally be emailed back to you in cleartext. If you choose not to enter a password, one will be automatically generated for you, and it will be sent to you once you’ve confirmed your subscription. You can always request a mail-back of your password when you edit your personal options.
Password choice: Confirm Password:
Would you like to receive list mail batched in a daily digest? (You may choose NoMail after you join.) No Yes

My question is this: is it possible to use the text widget for a form entry of this kind? If so, what should I be doing differently to get it to work?

If it’s not possible, how does one normally add an entry form for a newsletter signup?