Little tears like that in a 10' won't make much difference. You can see how the mesh slides into that channel, and maybe with some loosening of some bolts you can slide that back into place, take a hammer and flat piece of metal if you want to straighten out the dings. A little fine wire will let you mend the small tears back. As long as the dish still has good overall shape it should do a good job.
That's a c-band only feedhorn in the picture though, the unused coax you mentioned would have been used to power a ku-band lnb.
You can go with that and just tinker with c-band for awhile, or buy yourself a c/ku feedhorn with polarotor (that blue box controls polarity of the signals). Or you can get yourself a c/ku lnbf, won't need that Toshiba to control polarity, but you will need it to move the dish, unless you buy one of those gbox actuator controllers. That's a nice analog receiver there too, but there's not a lot of analog video left up there to see. See how this hobby works, now? One part begets another lol. That looks like the makings of a good beginning though. Good find.
edit: Added: the other questions, about the cable, I didn't address. YOu'll need a run of RG6 to power the lnb, if you didn't get the ribbon cable with the dish. If you use the analog receiver to power the lnb and polarotor, you'll need wire to operate the polarity motor too, you can buy sprinkler wire that'll handle that 5volts. May be able to use the same thing to power the dish-actuator motor. I think that's what I used on my last one that I rigged from parts. That ribbon cable can still be had, but I don't recall from where right off. Hope this helps get you started. Did you get the pole to put the dish on? If not, you'll need a 3.5" OD pipe to plant it.