Please help a dullard with custom views on single pages.

Sorry, but I am plain STOOOPID still with WordPress. All I want to do is things like this: have a search bar in the Right Widget, but only for the page called Blog, not all the pages. Have Categories (which I can’t even find in my widget list) in the right column widget, but only for the blog page- not all the pages…It seems any widget customizing has, with the exception of Home, global effects on all my pages.
I’m extremely embarrassed to include this information, but my blog page is here.

although it’s nothing at all like what I want it to look like yet.

I’d like to keep Home static, and the other pages are probably going to heavily modified or eliminated in the next couple of weeks…
Thanks anyone for helping poor me. I’m indebted.