In Shafi’ School does one get reward of praying taraweeh even though he has many qada prayers such as of Asr as its Haram to pray back when one has qada. I can’t make make intention for qada fasts before Ramadan due to doubts, is it valid?
One gets reward for any worship but in your case it makes no sense because you are putting aside what is both (i) urgently owed and accountable (and we do not know when Allah calls us back to Him) and (ii) more rewarding beyond comparison: in the Shafi`i school all the non-witr nafl prayers put together do not amount to the reward of one witr prayer, not to mention one fard prayer. Therefore the fulfillment of your fard supersedes everything else.
Tarawih provides you the opportunity to pray behind the imam with the jama`a while intending qada’ of fard, which is valid in the Shafi`i madhhab. Just make intention of qada‘ of fard at the ihram and, after the imam’s conclusion of his two rak`ats of tarawih, get up for the last two of your four rak`ats of qada’.
As for your second question, just focus on the fard fasting at hand together with sincere repentance for any past neglect of previous fard fasts, and make up the latter’s qada’ and fidya promptly after Ramadan.
Hajj Gibril Haddad