It really depends what app you have as to how it works. Mine is the 1.9 version, and all the options are along the top. Notifications, upload a photo etc. Click on them, have a fiddle and see how they work. Just experiment really. If you click on friends and go onto their profile page you will see an icon like a pointing finger...that does the pokes...
The 2.0 version is very much like the one I have on the Android. Click on the word Facebook and it should take you to a 'box' of options....your profile, messages, photos etc and most stuff can be done from there.
You could always go into your files, pictures, then choose a photo, click on it so it gets large then click on menu and the option is in there to 'share' with Facebook.
If you go onto Friends then you should see some options, either as small symbols or something to poke, tag etc.
Without seeing what app you have I'm only guessing that your's is the same as one of mine.... M.FACEBOOK
For the m.facebook if you click on Friends at the top of the page, then you get a list of your friends....choose the friend and click on their name which takes you to their profile.....then scroll right down to the bottom of the page and you will see a list of options....poke, message etc.
On your own page, if you scroll right down to the bottom there are all your options, notifications, places, groups events photos etc.
To post a pic off m.facebook, look just underneath where you would make a post and it says photo. Click on that and you get the option to browse....that will take you to your photos and you can upload. You can also put a comment on with the pic.
I'm wondering to if you have the setting set right for the notifications. Go onto MENU....OPTIONS....and tick the boxes that say messages to go into your message box, and tick Facebook notification. There are two more options in there, one to contact with out contacts,....which I haven't done, and one to conect with the calender again which I havent done.
Anyway, you are probably more confused now than you were before...lol.
Just click on stuff, experiment and find your way around bit by bit...