I bought engine transmission out of 82 to install in my 78. I got the crossmember with it. Will it bolt to the 78 frame ?

If the '78 frame came with an auto tranny, then it probably will.  I'll try to remember to check my old parts catalog. 

IIrc, the '68-'79 crossmembers will interchange. In '80 they went to the 350 transmission until '82, when the only trans was the 700R4. You CAN use your original crossmember, however...assuming you have an automatic trans car. The only modification needed is to slot the two bolt holes for the trans mount bolts, as the 700 mounts just a wee bit farther to the rear. Done plenty of 700 swaps in the earlier cars, and sometimes the bolts holes line up fine, and sometimes they need to be filed/ground out a little.