Is x86-64 is just an alias of EM64T?
Q1-does it mean that x86-64 is just an alias name of EM64T?

The original name for the architecture is AMD64.
That is also the marketing name that AMD uses for that architecture.
When Intel licensed it from AMD, they first called the feature CT, then IA-32e, then EM64T, and most recently Intel 64. Those are Intel's marketing names. Note that Intel 64 contains extensions on top of AMD64 as well.
x64 is not an official name. It is a marketing name created by Microsoft in order to refer to both Intel's and AMD's (as well as other vendors') implementations without using the name of one of the two main competitors.
x86-64 is not an official name. It is a marketing name used by many vendors in order to refer to both Intel's and AMD's (as well as other vendors') implementations without using the name of one of the two main competitors.
x86_64 is the GNU Autotools architecture designation used in tools such as Autoconf, Automake, and GCC.
IA-32 is, I believe, a term that Intel only introduced after they started working on IA-64. Until then, the architecture was colloquially known as x86, but did not actually have a name.
The bottom line is that you can mostly use the terms AMD64, IA-32e, x86-64, and x64 interchangeably, and people will probably understand what you are talking about. But, the official name for the architecture is AMD64, but that can also refer to AMD's specific implementation of that architecture (which may have AMD-specific extensions). Whereas IA-32e is Intel's specific implementation of the AMD64 architecture, which may have Intel-specific extensions.

Q2- And is IA32 developed by AMD?

No, it isn't.

isn't IA32 designed by Intel and first implemented in the 80386 microprocessor in 1985?

Yes, it is, although the name IA-32 came later.