Google organic search and Amazon affiliate links - are there going to be issues?

Here is my scenario guys. I have a completely new (1 month old) generic site about a similar set of activities:

- Each inner page is dedicated to a certain activity.
- Each inner page has good on page SEO and is ranking on decent positions considering the site is new and i haven't yet began to seriously build backlinks to it.
- Some of these pages i was thinking of monetizing with Amazon affiliate links in this manner:
A. insert generic sell text somewhere on page: "If you like this [X activity] and would like to buy this [X related product] you can check it out here:"
B. insert a well visible "button.jpg" image underneath, hyperlinked to one of my amazon affiliate links.

There are 4 questions that arise and I would like one of you SEO gurus to enlighten me if you can, because I do not have the knowledge:

1. Will google ruin that page's organic ranking position? (I have read somewhere that google hates affiliate links. I have done a good job at on-page-SEO for these pages. Will adding a "button.jpg" amazon button somewhere on the page and the "check it out here" text destroy my organic position of those pages?)
2. Should these "button.jpg" hyperlinks to the Amazon affiliate links be "nofollow" ?
3. Should i use Bitly or TinyURL to shorten these Amazon affiliate links so that Google Crawlers do not recognize them when they crawl my page?
4. Or should I just make one separate "[Generic Buy PRODUCTS]" page that contains all the products, and then make do-follow in-links from my different pages to this one single lame affiliate page? example: if you like [X activity] and you want to try it out check out the [Generic Buy PRODUCTS] page.

Why did i ask all this?
Because right now i am having the [Generic Buy PRODUCTS] page with in-links from the other site-pages to it. As I told you, my other pages are ranking ok.

But I am thinking that linking with a visible clickable and tasty "Buy on amazon" button on each page will convert way more than having some text links to the one single sell page (or even worse cos in my case my strategy is actually "check videos page" and under each video i have "check generic buy products page" - so it is two clicks away to get to my sell page).

But in the process of adding these buttons I don't want to destroy my organic search positions. Please advise me and answer each of the 4 questions above. I would really like to know this for the long run. Much appreciated !