As far as I know, only JH7 has had plans for a free-fall nuclear bomb. However, since the F-2 can already drop nuclear bombs, it is reasonable for them to make one for the J-10. After all, they themselves have stated that they strive to make each country have a “unique” nuclear bomber. Theoretically, there is no difference between the hanging points of small tactical nuclear bombs and conventional bombs. I believe that the J-10CE exported to Pakistan will replace the previous nuclear bomber to perform related missions
J-10A needs a compatible weapon, within the mass & dimension restrictions of the J-10 platform.
F-2A is lucky that B61 fits that requirement, and B61 is sadly not an option for PR-China, but is for RO-China.
So China needs something within the mass & dimension restrictions of the J-10 platform, and it has to be the J-10A since Gaijin is prioritizing fast-ish accelerating 13.x aircraft for this.
Yes, they are working on something new, most likely the J10. Currently, using the F16 as a temporary replacement is a good choice