Is there a Mathematician in the house?

yes,

and its prime 

and it's the sum of three other palindromic numbers

and those three palindromic numbers themselves are prime

and is the smallest prime that can be represented by the sum of a prime and its reversal: 383 = 241 + 142.

and it's a Woodhall prime 

and it's the only know multi digit Woodhall prime

and it's sexy prime (look that one up)

well done Wilson, I wonder who'd spot that one first

It's a sexy prime twin too! Yes, here is the  sexy prime 'bedfellow' for 383

 389

Really wanted it to be a sexy prime triplet but alas not it does have a cousin prime too though! Look that one up!

Mickeysf, surely the reason base ten is the norm is because we have ten digits on our hands.

What do you call a judge without thumbs? Justice fingers of course!

Which number is the odd one out - and why?

6, 22, 40, 51, 57, 77, 81

Many thanks for your attempts at solving the question.

You'll love this.

The answer is 40 – all the others come with Rice.

I'll get my coat.

40 is sweet & sour King prawns on the menu I'm reading, it comes with boiled rice but you can pay extra to change that to fried rice. 

6 is also an odd one out as its a single digit number. It's also prawn toast (without rice) 

81 is also an odd one out as its Chicken Maryland and as such is the only one which is not a Chinese dish.

Can any one fill in the spaces and explain this sequence.

...._,13,_,34,_....

The key to the middle number may open the door to the puzzle!

If I said I knew the answer to that would you think I was telling fib(onnaci)s, mickey?  

Yep, on an upward spiral!