I put the gift in the welcome email. I don't secure it, but I put some links in the ebook so that if it is shared I can still profit from it.

Yep, have your people who join your list get your ebook on the Thank you page or with the first email message in your auto-responder. No problem if your ebook gets shared with others, have your ebook contain links that lead them back to your landing page so they may return and opt in to your email list.
Best wishes

If you are using Aweber, you can send them to another landing page which says something like, jst enter your email to confirm your identity, or just have a button to the PDF link. If the user came through your initial Email (which means he/she already signed up) they will be given access to the download, else Aweber will get them through the signup process again.
This will secure your link to only the ones in your list.

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If people signup on your landing page with a garbage email you don't want to provide access to your PDF. Which is why double optin confirms that the person added to your list has a responsive email you can mail to. At this point you can provide direct access to the PDF in your sign up autoresponder mail with no download page. The problem with double optin is the fact that 50% of your sign up attempts will not respond to the confirmation email. This makes the cost per lead (CPL) more expensive!

Most people build their lists without double optin. In this case if someone signs up with a doggy email they will not get access to the PDF because the thank you page tells them to read the email you just sent them. That email can contain the PDF or link to a download page providing a link to the PDF.

No worries about the download page! A sharable download page is more desirable providing the PDF has embedded links to your front end offer and access to a landing page to get new subscribers. A lockable content PDF would be ideal if you could unlock the content by users virally sharing it with others.

We should have to put the gift offers for making the customer in new networking business because of it the customer influence

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Question 1 - create landing page for downloading the ebook and put the url of this landing page in the welcome email - Definitely.
Question 2 - Only allow the download once they have filled in the form with their details.

You can have your eBook put on a cloud service such as Dropbox or any other. The link is really hard to guess then and you can easily just send it to the subscribers.

I have few eBooks on leanpub.com and I send the link to that book with the coupon code applied to it.

If you are going to offer giveaways and you are using WordPress, there is a simple giveaway plugin "Simple Giveaways" which is free and it operates similar to KingSumo Giveaways (I have coded it).

In there, you could create a simple winner email template that will be sent to the winners of the giveaway. That email template could have a link to your file (preferably a cloud service of some sort).