2000 mazda codes po710 and po113

SOURCE: 1991 mazda mpv

I forget where I read this but if the tranny has been rebuilt they could have put the wrong bolt in the wrong hole. All the bolts are the same size except for one long one. If you put the long one in a short hole it will kill 3rd gear and it may need to be rebuilt.

SOURCE: 1997 Mazda protege transmission, Hard shifting from 1st gear

I would try a flush. If its set up like my 96, and it likely is, changing the trasmission gasket and filter will be difficult. Mine has a medal plug on the bottom and takes an allen wrench, and possibly a breaker bar. If you take out this plug, drain, flush then refill via the dipstick tube and a funnel, it may help. You may need to do this a couple of times due to fluid still in the torque converter, pan, etc.
Lucas is good stuff, I would add it again when I was done. The tranny fluid should be pink, mine looked like used oil black before I flushed it.
Also, when adding the new fluid, shift slowly up and down through all of the gears to lube well and check your fluid levels after 100 miles or so, as sometimes a bubble will form and make it look full....then not after it pops.

SOURCE: mazd mpv cranks sometimes starts sometimes nothing

I would check the ignition control module. It may be firing and missing intermitinly

SOURCE: Transmission maintenance

Service trans every 2 years or 24,000 miles.Buy a trans filter kit,remove trans oil pan,replace or clean filter(some tranys has a wire mesh screen in them that is cleaned,not replaced),replace oil pan & refill with recommended amount & proper type of fluid.REMEMBER THIS:CLEANLINESS IS GODLINESS WHEN WORKING ON AUTO TRANS,DON'T LEAVE ANY PIECES OF RAGS OR ANY OTHER MATERIAL INSIDE OF TRANS!!!

SOURCE: 1990 mazda mpv power steering pressure switch

You can try a junk yard or better yet the dealer for new.