Since they are together as a single scroll this poses a complex problem the Rashba brings a Teshuva regarding books of the chumash that were written separately and without being done leshem kedusha(which would in any even possul the sefer Torah from being used) part 1 chapter 144 writes
אם הם כגולל וכתקנן, הרי הם בספר תורה לכל דבריהם, אלא שאין קורין בהם
בצבור, מפני כבוד הצבור בלבד.
If they are rolled and attached, behold they are a Sefer Torah in all
respects, only we do not read from them in front of the congregation,
and that is only on account of the honor of the congregation.
The Taz(Y"D 271:8) and the Beur Halakha aka the Chafetz Chaim(83:5) also seem to regard printed seforim, on an equal level of holiness with scribed seforim, and thus the above worries of the Rashba would apply.
From an article on Torah.org regarding printed seforim:
With the advent of the printing press in the fifteenth century, the
Torah authorities of the time debated whether printed sefarim had the
same level of kedushah as handwritten works. The consensus of the
poskim was that a printed sefer is to be treated no differently from a
Further you have an interesting, even if widely rejected Teshuva by Rav Abadi that deems use of a printing press to actually be preferable to the use of scribe in writing a Sefer Torah. Which if correct would leave only the issue of it being printed on paper as a possible disqualification of being a genuine Sefer Torah.
Finally Rav Ovadia Yosef wrote a lengthy Teshuva on the issue of these gift scrolls in his journal Or Torah from Av 5762, in which he goes through the various opinions regarding how the scrolls should be treated, and whether damaging them is on the same level as damaging an actual sefer Torah. It's really worth a read if you can get hold of it. In short he goes back and forth and ends with, those who are stringent will merit a blessing, but doesn't actually settle on a final decision in that regard. Regarding what to do with however, he says clearly that it is necessary to entomb it.
In that respect, regarding whether it can be fixed, it would depend on where the rip took place. If it happned in the margin, then, like a normal Torah Scroll it could be fixed. If it tore through the words, while technically one could replace the torn panel, it would seem by and large it cannot be fixed and would have to be entombed just as an irreparable Sefer Torah.
Whether one needs to fast and such as is normal when damaging an actual Sefer Torah, again from this it would seem that such is the case, however one should ask a reliable posek.