Can I use a package of Apache-1.1 license and a package of Apache-2.0 license and distribute the resulting package under Apache-2.0 license? Is there a conflict between Apache-1.1 and Apache-2.0?
The Apache-1.1 and Apache-2.0 licenses are both fairly permissive open-source licenses. Neither of them tries to extend their influence beyond the code that is explicitly licensed with either license and neither contains requirements that is incompatible with the other license.
This means that the two licenses are compatible with each other and it is possible to have code licensed under Apache-1.1 together with code that is licensed under Apache-2.0 in a single project.
The Apache-1.1 license does not allow sub-licensing or changing the license to a later version, so if you create a package that contains a mix of Apache-1.1 and Apache-2.0 licensed code, then you must keep the Apache-1.1 licensed code under that license and you must make it clear that different copyright licenses apply to different parts of the package.
This is especially important for the Apache-1.1 license, because it has specific acknowledgement requirements that users of your package should be aware of.