Difference between strong interaction and weak interaction?

Can there be a strong interaction in which transformation of one quark flavor into another takes place (Eg. up quark → down quark)?

No. Flavor is a good quantum number.

In charged current weak interactions, flavor is violated, whence the ditty that strangeness is produced strongly (in S=-1+1=0 associated pairs), but decays weakly: strangeness weak-decays to upness.

Can there be a weak interaction in which transformation of quark flavors doesn't take place?

Yes, of course. Weak neutral currents, coupling to the Z boson, do not violate flavor.

If both the answers are "No", then while checking a nuclear reaction/decay can't we just match quarks on both sides(by cancelling extra quark and anti quark pairs) and if same number of different quarks are present than it will be a strong interaction and it not than a weak interaction(provided other conservation laws are followed)?

No, you saw why you can't just do that, as your premise fails. In NC neutrino scattering, flavors are conserved.

If leptons are present in a nuclear reaction/decay does that necessarily mean that the reaction is a weak interaction?

Only for neutrinos. The reaction won't be strong, but an electron-positron pair could be a converted photon, so EM.

If photons are involved in a nuclear reaction does that mean that it's an electromagnetic interaction?

There could be other things happening, but certainly the photon came out of an EM coupling/vertex.