If a site links to one of my inner pages,does it count as a weaker backlink compared to the index page because the keywords in my index page is better placed and the keyword that i am targetting is in the 1st position in the title of the index page?
If a site links to one of your interior pages (not the home page) then it really has the same effect as if they were to link to your home page. In fact, I prefer to have links to my inner pages rather than just the home page. It will help the inner pages rank better, and since I have good navigation on the site, link "credit" is passed around just fine. Whether or not the link is a good link or not depends on the other site, whether or not the link is on topic, and what type of link it is, not necessarily where they link to. If it's a straight text link that's on topic to your inner page, then that's a great link to have.
It depends. If thats not the main page your working at then it could be a weaker backlink only in your terms. But if it was to a page that is important then it is a more significant backlink.
As long as it's easy navigation to your main page then any backlink is a good link in my opinion. If you have any say in it, make sure the link text is specific for the keywords on that inner page and not your more general keywords for your mainpage.