apk file is might be big because of your resources , splash image and icons image . Their size must be really big . Please use a low sized image to generate your resources .
for profile issues please follow :
this is a hosting security related issue . Some server strips the authorization parameter which is sent in headers due to security reasons (I dont know why ) .
put this line in your .htaccess file at the end (.htaccess can be found in root of your site ):
SetEnvIf Authorization .+ HTTP_AUTHORIZATION=$0
IF above does not works then please change the above line to :