magento link not working (broken) after migration (server to server) - .htaccess

Question

i have a lot of trouble with a migration.
I have moved a beta website to the definitive server:
shopfair.eu/
after a lot of issue, i have still 2 problems:
first of all, all the pages are corrupted (not accessible) i.e.
http://shopfair.eu/index.php/alimenti-ipocalorici/linea-lazero.html
i have noticed that if i remove /index.php/ from the bar the page exist and is working
http://shopfair.eu/index.php/alimenti-ipocalorici/linea-lazero.html
The other problem is that i cant acces the Admin page... and seems due to the same issue.
I think its an .htaccess or rewrite problem.
Thanks in advance.
my .htacces:
`############################################
## uncomment these lines for CGI mode
## make sure to specify the correct cgi php binary file name
## it might be /cgi-bin/php-cgi
# Action php5-cgi /cgi-bin/php5-cgi
# AddHandler php5-cgi .php
############################################
## GoDaddy specific options
# Options -MultiViews
## you might also need to add this line to php.ini
## cgi.fix_pathinfo = 1
## if it still doesn't work, rename php.ini to php5.ini
############################################
## this line is specific for 1and1 hosting
#AddType x-mapp-php5 .php
#AddHandler x-mapp-php5 .php
############################################
## default index file
DirectoryIndex index.php
<IfModule mod_php5.c>
############################################
## adjust memory limit
php_value memory_limit 512M
php_value max_execution_time 18000
############################################
## disable magic quotes for php request vars
php_flag magic_quotes_gpc off
############################################
## disable automatic session start
## before autoload was initialized
php_flag session.auto_start off
############################################
## enable resulting html compression
#php_flag zlib.output_compression on
###########################################
# disable user agent verification to not break multiple image upload
php_flag suhosin.session.cryptua off
###########################################
# turn off compatibility with PHP4 when dealing with objects
php_flag zend.ze1_compatibility_mode Off
</IfModule>
<IfModule mod_security.c>
###########################################
# disable POST processing to not break multiple image upload
SecFilterEngine Off
SecFilterScanPOST Off
</IfModule>
<IfModule mod_deflate.c>
############################################
## enable apache served files compression
## http://developer.yahoo.com/performance/rules.html#gzip
# Insert filter on all content
###SetOutputFilter DEFLATE
# Insert filter on selected content types only
#AddOutputFilterByType DEFLATE text/html text/plain text/xml text/css text/javascript
# Netscape 4.x has some problems...
#BrowserMatch ^Mozilla/4 gzip-only-text/html
# Netscape 4.06-4.08 have some more problems
#BrowserMatch ^Mozilla/4\.0[678] no-gzip
# MSIE masquerades as Netscape, but it is fine
#BrowserMatch \bMSIE !no-gzip !gzip-only-text/html
# Don't compress images
#SetEnvIfNoCase Request_URI \.(?:gif|jpe?g|png)$ no-gzip dont-vary
# Make sure proxies don't deliver the wrong content
#Header append Vary User-Agent env=!dont-vary
</IfModule>
<IfModule mod_ssl.c>
############################################
## make HTTPS env vars available for CGI mode
SSLOptions StdEnvVars
</IfModule>
<IfModule mod_rewrite.c>
############################################
## enable rewrites
#Options +FollowSymLinks
RewriteEngine on
############################################
## you can put here your magento root folder
## path relative to web root
RewriteBase /shopfair.eu/
############################################
## workaround for HTTP authorization
## in CGI environment
RewriteRule .* - [E=HTTP_AUTHORIZATION:%{HTTP:Authorization}]
############################################
## always send 404 on missing files in these folders
RewriteCond %{REQUEST_URI} !^/(media|skin|js)/
############################################
## never rewrite for existing files, directories and links
RewriteCond %{REQUEST_FILENAME} !-f
RewriteCond %{REQUEST_FILENAME} !-d
RewriteCond %{REQUEST_FILENAME} !-l
############################################
## rewrite everything else to index.php
RewriteRule .* index.php [L]
</IfModule>
############################################
## Prevent character encoding issues from server overrides
## If you still have problems, use the second line instead
AddDefaultCharset Off
#AddDefaultCharset UTF-8
<IfModule mod_expires.c>
############################################
## Add default Expires header
## http://developer.yahoo.com/performance/rules.html#expires
ExpiresDefault "access plus 1 year"
</IfModule>
############################################
## By default allow all access
Order allow,deny
Allow from all
############################################
## If running in cluster environment, uncomment this
## http://developer.yahoo.com/performance/rules.html#etags
#FileETag none`

Answer 1

Yes, You've rewrite problem. Please make sure your .htaccess file contain below code. If not then please change it.
Please check below code in your .htaccess,
<IfModule mod_rewrite.c>
############################################
## enable rewrites
Options +FollowSymLinks
RewriteEngine on
############################################
## you can put here your magento root folder
## path relative to web root
#RewriteBase /magento (Your Magento Root Folder)
############################################
## uncomment next line to enable light API calls processing
# RewriteRule ^api/([a-z][0-9a-z_]+)/?$ api.php?type=$1 [QSA,L]
############################################
## rewrite API2 calls to api.php (by now it is REST only)
RewriteRule ^api/rest api.php?type=rest [QSA,L]
############################################
## workaround for HTTP authorization
## in CGI environment
RewriteRule .* - [E=HTTP_AUTHORIZATION:%{HTTP:Authorization}]
############################################
## TRACE and TRACK HTTP methods disabled to prevent XSS attacks
RewriteCond %{REQUEST_METHOD} ^TRAC[EK]
RewriteRule .* - [L,R=405]
############################################
## redirect for mobile user agents
#RewriteCond %{REQUEST_URI} !^/mobiledirectoryhere/.*$
#RewriteCond %{HTTP_USER_AGENT} "android|blackberry|ipad|iphone|ipod|iemobile|opera mobile|palmos|webos|googlebot-mobile" [NC]
#RewriteRule ^(.*)$ /mobiledirectoryhere/ [L,R=302]
############################################
## always send 404 on missing files in these folders
RewriteCond %{REQUEST_URI} !^/(media|skin|js)/
############################################
## never rewrite for existing files, directories and links
RewriteCond %{REQUEST_FILENAME} !-f
RewriteCond %{REQUEST_FILENAME} !-d
RewriteCond %{REQUEST_FILENAME} !-l
############################################
## rewrite everything else to index.php
RewriteRule .* index.php [L]
</IfModule>
2) The above code is working perfect in many projects. If it doesn't solve your issue. Try to make your .htaccess file like this-->
https://github.com/Creare/magento-htaccess/blob/master/.htaccess
If you can share your .htaccess then i will better solve your issue.
Regards.

Answer 2

Because of the disabled function FollowSymLink and +SymLinksIfOwnerMatch on my server, i added the following code to my .htaccess
<IfModule mod_rewrite.c>
RewriteEngine On
RewriteBase /
RewriteRule ^index\.php$ - [L]
RewriteCond %{REQUEST_FILENAME} !-f
RewriteCond %{REQUEST_FILENAME} !-d
RewriteRule . /index.php [L]
</IfModule>
then deleted all the files in the var/cache and var/session folder.
After that the site is working, but the admin now seems not working (blank page).