Any change on a site will change its ranking. That is an easy logic. But some changes have big impacts. They are as below in order; change in the name of your site title content meta description link structure link places on the page(s) hosting placement + machine/network speed meta keywords HTML + http header (character set, etc.) CSS whois info of your site's domain
If the content has no changes, the effect will be small. If the content is redesigned too, the change could be much bigger.
I think it would be effected. The position of the content in html changes and might affect your rankings.
Most of it will affect. Because most of time you think you didn't change contents but you did move their orders. It is just like you redesign your living room you move TV to another corner. Actually it is a big move.
Well i will say changing theme will not effect ur ranking, if this change is for template only but what ihave noticed is that most of the high ranking sites dont change thier templates even after many years so u can take risk at ur own.
I guess, on balance, I'd rather have visitors to a site that might need a bit of work on it, rather than have a top looking site and no SERPS.
Changing the design CAN affect your SERPS as the way your text is arranged on the page affects SERPS as well.