I'm answering here with three hats on... as a parent of four, a granny to a 3.5 yr old, and as someone who has worked in Early Years for 20 years :)
Speech sounds... MANY MANY 3,4 and even 5 year olds had difficulties with certain sounds. Immature speech generally improves gradually and as Nursery have said they will help her practise, that' a great start. I spend my days with children who are mostly 4 and 5 and quite a few have difficulty with certain sounds. My own DD1 couldn't say 'c' sounds (a cucumber was a 'humhumber', a can of coke was a 'han o hoke' ) when she was 4. We enquired about speech therapy but by the time she was seen it was resolving (and she's now a doctor..a GP and speaks perfectly well)
My grandson is 3.5 and struggles with quite a few sounds, and sometimes is a little tricky to understand. We repeat the tricky word back to him..sometimes he will try and copy, sometimes he won't, and that's ok.
3 and 4 year olds are tricky creatures. They are becoming more independent and also, frequently, are wrestling with control.. they want what THEY want. And that frequently means not answering, not responding. I care for my grandson several days a week and I don't think I've ever had what I would call an appropriate answer to 'what did you do at Nursery today?' Often I get 'I don't know'! (sometimes he'll tell me hours later )
Tantrums.. yes. The easy 2 year old becomes a less easy 3 year old and a stroppy, uncooperative beastie at 4. Normal. Boundary testing! It's really frustrating, and yes some children are easier than others, but it's not abnormal... they are becoming much more aware of their own feelings and those feelings can be HUGE and irrational.
The belly button thing made me laugh... because my grandson is EXACTLY the same! Even as a baby we had to stop putting him in baby grows or pop under vests because he was distraught if he couldn't get his finger in it when he was tired or needed to self soothe (never had a dummy as he wouldn't take one) he goes into another zone when he does that too, but it's no different to a child sucking their thump or rubbing their ears, it's just a rather individual soothing tool...and at least they can't lose their belly buttons 
Honestly nothing you have said stands out as unusual. Children vary wildly in their speech development ..understanding is far more critical than clear production as a guide to when to worry.
In my personal and professional experience, speech difficulties tend to even out by 5 and they also become a lot more reasonable as human beings :) The belly button habit may however persist !
My DS2 had a severe speech and language delay (speech therapy and special school) ..no speech at all until he was 4. He's an adult now, very articulate and intelligent and you would never know :)
Sorry, that was awfully long but I hope reassures you a little!