No, the bot only works with channels.

Yes, the bot works equally with private or public channels.

To use the bot, just add @publishareBot to your Telegram channel as you would do when you add a new user.

To uninstall the bot, just remove it from users. Easy.

• Once installed as written above, go to chat with the bot and select the /list option from the menu, or simply write and send the command /list. It will prompt the channels' list where you have installed the bot in.
• Select the channel you want to manage from the list.
• Select the option Your own website.
• Select the option Insert (or Edit if site was already linked).
• Write your endpoint link and send it to the bot.
• If you don't know what an endpoint is, just read the following question.

An endpoint is a special link of your website where the bot will send data to.

If you don't know how to set an endpoint, just read the following questions.

If your website is built with WordPress, I just developed a plugin to do that in a breeze and without any programming skill.

If your website is NOT built with WordPress, you should probably ask your web developer or someone else who can code, sorry. :/

The next question will explain how to technically configure an endpoint in that specific case.

The endpoint needs to manage the following HTTP methods: POST, PUT, DELETE with their related set of data

• POST (to publish a new message)
  The endpoint will receive a JSON payload with the following data

  {
  	"id": THE_ID_OF_THE_MESSAGE,
  	"title": THE_TITLE_TEXT_OF_YOUR_POST,
  	"text": THE_CONTENT_TEXT_OF_YOUR_POST,
  	"base64Photo": BASE64_ENCODED_PICTURE
  }

• PUT (to edit a published message)
  The endpoint will receive a JSON payload with the following data

  {
  	"id": THE_ID_OF_THE_MESSAGE,
  	"title": THE_TITLE_TEXT_OF_YOUR_POST,
  	"text": THE_CONTENT_TEXT_OF_YOUR_POST,
  	"base64Photo": BASE64_ENCODED_PICTURE
  }

• DELETE (to delete one or multiple published messages)
  The endpoint will receive a JSON payload with the following data

  {
  	"ids": [
  		ID_OF_MESSAGE_X,
  		ID_OF_MESSAGE_Y,
  		ID_OF_MESSAGE_Z,
  		...
  	]
  }

• Chat with the bot and choose the /list option from the menu, or simply write and send the command /list. It will prompt the list of channels where you have installed the bot.
• Select the channel you want to manage.
• Select the option Your Twitter account.
• Open the Twitter auth link and confirm access from your Twitter account.
• Once given the authorization is given, all the new posts from your channel will be published on your Twitter account too.

IMPORTANT NOTE

Publishing on Twitter has some actual limitations:

1. It's not possible to modify a tweet (you have to delete it and resend in that case).
2. It's not possible to delete more than 12 tweets in the same time.
   In that case, only the first 12 will be deleted.

Actually there is yet no integration with the Facebook, Instagram and other social's API. They are in the plans, anyway.
Any funding support would be sure of great help.

Telegram gives you the possibility to format your text. For example you can format a text as bold.
So, to set a title on your post, just format as bold the INITIAL PART (won't work if not at the beginning) that you would like to be the title.
That delimited portion of text will be automatically separated from the rest of the text and marked as a title when sent, for example, to your personal blog.
NOTE: the title will not apper on Twitter.

The service it totally free and is going to work with donations. So, if you like it, any donations will be really appreciated. To support the development and the server costs you can donate here.

Unluckily, there is some lack with Telegram and the service won't get a real time update after deletion.
To solve this, you can just edit an existing post of your channel (eg. by adding a like or editing some text) in this case the "delete" event will be immediately fired with the new update.
So sorry for this inconvenient, but it's not due to the present service. Let's hope Telegram will fix this soon.