May a single Parsha be written in two different Kesavim, such as Beis Yosef and Arizal?

Some Poskim[1] rule that the Tefillin are invalid in such a case. Majority of Poskim[2], however, conclude that they are valid. Initially, however, the Parshiyos are to be of the same script.[3]

May one wear the Shel Yad of one Kesav, and Shel Rosh of another Kesav?[4]

Yes. However, it is best for both Tefillin to be of the same script.

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[1] Mishnas Avraham 83:28 that so ruled all Gedolei Poland due to Tarta Desasra; Igros Moshe 4:9 [in letter to Rebbe] that it is invalid due to Menumar; See M”A 32:49

[2] Heishiv Moshe Y.D. 51; Giddulei Hakodesh 15:30; See Shut Rav Akiva Eiger Tinyana 5; Shoel Umeishiv 3:226; Maharsham 2:120

[3] See Likkutei Sichos 39:244, printed in Shulchan Menachem 1:71, that the Kesav of the entire Tefila is to be a single Nussach.

[4] See Heishiv Moshe Y.D. 51; Imrei Shefer 5; Halichos Shlomo 4:22; Piskeiy Teshuvos 36:1 footnote 5; See Likkutei Sichos 39:244, printed in Shulchan Menachem 1:71, in reply to the question of whether one can wear Rashi Tefillin with the knots of Ashkenaz and Rabbeinu Tam with the knots of Chabad, the Rebbe replied that this is dependent on his feeling, although in any case the knots of both Tefillin, and the Kesav of the entire Tefila is to be a single Nussach. It is unclear from this reply if the intent is to say that both the Shel Yad and Shel Rosh should be of one Kesav, or if they may be of different Kesav, so long as they are not of two different Kesav on their own