Yes on the first question.
Your 1.1 apps will continue to work under 1.1

No on the second question.

You may *create* new 2.0 apps, but your old apps will only be able
to process 1.1 classes, unless you upgrade the app to use the 2.0
framework by using the ASP.NET tab in the Internet Service Manager's
"Properties" for the application.

In that case, *all* of you application will run under 2.0.

You cannot have the same application run 1.1 and 2.0 classes concurrently.

Juan T. Llibre, ASP.NET MVP
ASP.NET FAQ : http://asp.net.do/faq/
Foros de ASP.NET en Español : http://asp.net.do/foros/
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Side by side is fine, as Juan has mentioned.

When you install the redist, I believe it leaves 1.1 for current webs (1.1
upgraded all 1.0 webs, so it operated a bit differently). You can also run
aspnet_regiis -i under the 2.0 directory and have all webs run under 2.0. You
can also selectively choose which run under which version of the framework
using the same tool or assigning individually in ISM, etc.

As long as you have not hit a rare forward breaking change, you can deploy
1.1 to 1.1 or 2.0, but realize that a recompile in 2.0 is the best way to go
if you are going to run under 2.0.

As for adding 2.0 pages to current apps? Only if you upgrade the app to 2.0.
You cannot have 2.0 built pages run under 1.1 when compiled for 2.0. You can,
however, develop in 2.0 and compile in 1.1, provided you use no new features.
Best best is to migrate 1.1 code to 2.0 and add the new 2.0 features and then
deploy to 2.0.