Hello.
First you need check your AbanteCart error log - you can locate error log directly in the file /system/logs/error.txt
Some errors may help to indicate what is wrong (for example http://forum.abantecart.com/index.php/topic,2573.msg10924.html#msg10924).
In case you have problem with Mail settings and your server can not send reset email try to change Mail setting in database http://forum.abantecart.com/index.php/topic,711.msg2481.html#msg2481

Also you can try a simple hack to get your temporary password to be displayed but this will work in case your mail is work.
http://forum.abantecart.com/index.php/topic,547.msg1681.html#msg1681

Hello.

You should update from 1.1.9 to 1.2.0 > 1.2.1 > ....> 1.2.5
Thant why your site broken.

About backup file http://forum.abantecart.com/index.php/topic,3522.msg15177.html#msg15177

Hello.
You can embed products or categories to almost any html or if you developers you can use AbanteCart API

Hello.

Banner slider works on tablets and smartphones but if your smartphone screen size is less then approximately 800px (phone assumed to be low resources) then slider replaced with static banner (managed in admin) to speed up home page on slow devices.

For the images size try 940px width images

Hello.

Can you please change admin language to English and check did you see same problem? Or PM admin access to me I will try to figure out what is wrong

But why you ask that? Must i translate it to english again?

No, You dont need to translate. I ask because think that something wrong with your language. But if you did not see in english issue in other place. Can you PM your admin access? I can try to find problem.

Create new product and check is it visible in admin

i didn't find an php.ini file in that folder. Are there other ways to solve it?

Ask your hosting provider support to help you. Server configuration is their issue