You want to put the prepositional phrase that modifies the noun immediately after the noun.
I think you didn't copy these sentences perfectly, because they all seem to have grammar issues. (In the future, if you want a faster response, please take care to make sure the sentences are copied correctly.) I've fixed these issues in the examples below:
That's the specialist in chemistry at the podium. [CORRECT]
That's the specialist at the podium in chemistry. [INCORRECT]
In chemistry describes specialist.
He is a contender with a shoulder injury for the Best Chef title. [INCORRECT]
He is a contender for the Best Chef title with a shoulder injury.
For the Best Chef title describes contender.
Question 3a and 3b hardly make any sense. They just seem to be follow-up questions to question 2. I've tried to fix them up:
Which title is he a contender for? [CORRECT]
Which part of his body is he contending with? [INCORRECT]
Technically, you can contend with a shoulder injury. But it's obvious here that the contender is contending for a title.
Note, you shouldn't end a sentence with prepositions. These sentences have numerous errors and make it very hard to comprehend.