Okay... Here goes a few tips:
(Q) How to delete your status? (A) On the right hand side of each status -- you should see three small dots. Tap on it.
(Q) How to download pics? (A) Tap on pic and press menu on device. Since you might not be able to download the pic directly, you can get the pic by sharing it to whichever application on your device ( this way you can download it to your device.) It could be an app, email, messaging...whichever works best for you.
(Q) How do I delete a friend's comment on my thread? (A) Unfortunately, this option isn't available anymore - you usually could swipe your finger from right to left directly over the comment to delete/remove it. However, this can still be done using the m.facebook.com or any other facebook app that supports this feature.
Edit: [ really hope they implement a way of deleting comment(s). Some comments I just don't approve of - and would be better not viewing by me or any of my FB friends.
I really don't have much problem with this app since the recent update. Could it be better? Yes, a lot better. Can I live with it the way it is now? Sure. But hopefully they get it together.
"Accept the things you cannot change, have the courage to change the things you can ...And have the Wisdom to know the difference".