(1)点F(p/2,0),E(3,2).设M(x1,y1),N(x2,y2),
MN的中点为E,
所以x1+x2=6,
M,.F,.N三点共线，
所以|MN|=|MF|+|FN|=x1+x2+p=6+p=8.p=2
所以抛物线方程为y^2=4x①
(2)设P(-1,m),直线l的方程为x=ny+t,②
代入①，得y^2-4ny-4t=0,
设A(x3,y3),B(x4,y4),则y3+y4=4n,y3y4=-4t.
由②，x3+x4=n(y3+y4)+2t=4n^2+2t,
x3x4=(ny3+t)(ny4+t)=n^2y3y4+nt(y3+y4)+t^2=-4n^2t+4n^2t+t^2=t^2,
x4y3+x3y4=y3(ny4+t)+y4(ny3+t)=2ny3y4+t(y3+y4)=-8nt+4nt=-4nt,
PA的斜率k1=(y3-m)/(x3+1),
PB的斜率k2=(y4-m)/(x4+1),
PT的斜率k3=-m/(t+1),
k1+k2=(y3-m)/(x3+1)+(y4-m)/(x4+1)
=[(y3-m)(x4+1)+(y4-m)(x3+1)]/[(x3+1)(x4+1)]
=[x4y3+x3y4+y3+y4-m(x3+x4+2)]/(x3x4+x3+x4+1)
=[-4nt+4n-m(4n^2+2t+2)]/(t^2+4n^2+2t+1),
所以k1+k2-2k3=[-4nt+4n-m(4n^2+2t+2)]/(t^2+4n^2+2t+1)+2m/(t+1)
={(t+1)[-4nt+4n-m(4n^2+2t+2)]+2m(t^2+4n^2+2t+1)}/[(t^2+4n^2+2t+1)(t+1)]
=[4n(1-t^2)+4mn^2(1-t)]/[(t^2+4n^2+2t+1)(t+1)]为定值，即与m无关，
所以t=1,定值为0，T的坐标为(1,0).
