Is there any way to determine variable type only by variable name (for example GetVarDeclByVarName(const char* var_name) or GetVarTypeIdByVarName(const char* var_name)? I'm implementing IDE for AngelScript and this functionality would be very helpful for me to write autocompletion and intellisense-like mechanisms.

Unfortunately not. You have to enumerate the variables to find the right one. Use GetVarCount and GetVar for that. Remember that multiple variables in a function may use the same name if they have different scope.

You need some sort of context for the the variable in order to get it's properties. For instance, if it's a module variable you can use asIScriptModule::GetGlobalVarIndexByName() to get the variable index and then asIScriptModule::GetGlobalVar() to get its type. Similarly there's asIObjectType::GetProperty() to get the information about a property's type and asIScriptFunction::GetVar() to get the type of a function's local variables.