How do I connect the Irulu keyboard to my tablet, besides by plugging the mini usb into the port on the side? Because my tablet doesn't recognize, that it is even plugged in.

normally keyboards like this may use bluetooth or USB connection to work if USB you can buy a USB-OTG cable to use the keyboard

I advise downloading the user manual from:
https://www.irulu.com/download-center-new

1 port is a mini hdmi port to connect to a tv via a hdmi mini to hdmi cable,the other is a mini usb port,with the data cable that you can buy for it,you can connect to a computer,not just any usb cable will work,there is 1 for charging and 1 for data Ematic Edan XL EGS109 9 Inch Tablet 5 ft USB 2 0 Mini Micro Cable

Juello. Did some research on your tablet at Amazon, (http://amzn.to/1xWx6S5) and see that they also have an AC charger (AC charger adapter with a 3.5mm power jack and delivering 5VDC 2A). Available for $5: iRulu Black AC Home Wall Adapter Cable Charger for Tablet PC 5V 2000mAh or a there's a nice replacement KB and cover: iRulu New Portable 10 1 10 5 Android Tablet USB Keyboard Case Black . I would guess the connector snapped off inside the tablet, so you will have to remove it with some tweezers. If the pin for the AC adapter broke off inside the tablet, that's a problem, but most everything can be charged from the USB port too see this website:
How To Charge Samsung Galaxy Tab 2 Via USB Port On Computer Laptop PCNEXUS (Samsung used as an example). GL

Not sure on you particular model but most tablets have 2 mini USB ports one has a power supply and the other is just an I.O port .

Try your keyboard in the other port if you have one and it should work. If not it may be faulty.
HTH

The biggest problem with tablets and phones is the micro USB socket. They are easy to break if you put them in the wrong way round and it is not always easy to see if they are connected correctly.
Check the USB plug and the the tablets socket are not damaged.
Check that USB keyboard works in another device and that another USB input device works in the tablets USB socket.
I am suprised it works at all. You state you are using Android 2.2 yet USB hostmode was only introduced with Android 3.1

There are some apps in the play store like USB device info which may help. For proper debugging you need an APK which is not for the average user. http://visualgdb.com/tutorials/android/usbdebug/
But cables and plugs are 98% of the problem
Good Luck

Your tablet is not built to accept usb keyboards.

am trying to connect with internet my device (irulu ak 305) but it didn't connect

Where can I find irulu tablet's kiboard user manual