The statements can be proven the same way as in [Gub10, Corollary 5.9]. In order to bypass the algebraically closedness of the base field one can use [Gub13, Proposition 6.22] instead of [Gub07, Proposition 4.4] for (a), [Gub13, Proposition 6.22] instead of [Gub07, Remark 4.8] for (e) and [Gub13, Proposition 6.14] instead of [Gub07, Proposition 4.7] for (f). ∎