Some problems with Zorin Gnome-desktop?

I read a praising rewiew of Zorin in the LINUX FORMAT magazine. So I downloaded Zorin OS 12.1 64-biand installed it to my old PC with ,
47 GiB MD Athlon(tm) 64 X2 Dual Core Processor 5000+ × 2 and
Gallium 0.4 on ATI RS690.

The desktop looks very nice but propably it is too heavy for my old computer. Do you recommend some other for me for. ex. Mate or XFCE?

And can I get some other desktop simply by intalling sudo apt-get install xfce or some other package?

There are also some problems:
I'm reading my local newspaper from http://www.kaleva.fi as facsimile. But unfortunately the Adobe Player is needed. Usually in the Ubuntu-relative Linuxes you get it by typing to the terminal:
sudo apt-get install ubuntu-restricted-extras.

But this time that magic trick did not help

I have some older computers as well and I can tell you Zorin OS9 runs fantastic on all of them.

As Zorin OS 9 is based on Ubuntu 14.04 LTS you can expect to receive continuous software updates until 2019.

So that is one possibility for you. I expect you will get more feedback throughout the day.

Try SolydX stable community edition which uses xfce - gnome shell and gnome 3 are too heavy.

Speaking as a complete amateur who has used Zorin OS for years, sorry you are having problems. When installing Zorin I have always included the extra CODECS at that time. The machine I am writing this on is similar to yours [Dell Optiflex 760 - Dual core E4400. 4GB RAM, Intel Graphics, 32bit. It runs Zorin 12.1 with no trouble. I have made some changes for 'cosmetic' reasons, to use Nemo instead of Nautilus for the desktop.]
Did you check the download?
If you install all Zorin updates it should give you the missing CODECS (see System Tools >Software and Updates).
If you still can't get things right, the new Zorin 12 Lite is due any time now (probably XFCE based).
Regarding your newspaper, I was able to see Kaleva with no problems using Zorin 12.1 including rather intrusive pop-up ads.