I made my first ASP application, the server that they provide to host my application has many applications running, but those existing applications were made with framework 3.5 and my application needs framework 4.5.2.
If I install framework 4.5.2, can I have a problem with the applications that already exist? Or can I do it without problems?
If you install the .NET Framework 4.5.2 the applications that were created for the .NET Framework 3.5 will try to run on the new framework.
In general it should not be a problem since in general the new frameworks are compatible backwards with the previous ones, however this is not 100% true.
Some security features and new flags on ASP.NET features that work correctly in the .NET Framework 3.5 may have been modified to improve performance or security and cause the application to behave differently or no longer work in particular .
If you want to guarantee that the previous applications keep running on the old CLR (CLR 2 in the case of .NET Framework 3.5) add this to the web.config of each of the applications
<configuration>
<startup>
<supportedRuntime version="v2.0.50727"/>
</startup>
</configuration>
Finally I recommend that you test all the applications again in a pre-production environment with the new framework before you do it in Production, to avoid inconveniences.