We present a new method that uses CCD images of the FERMI electron beam at the dump spectrometer after the undulator to determine various electron beam and external seed laser properties. By taking advantage of the correlation between time and electron beam energy for a quasi-linearly chirped electron beam and the fact that the FERMI seed laser pulse (~180 fs) is much shorter than the electron beam duration (~1 ps), measurements of the e-beam pulse length and temporally local energy chirp and current are possible. Moreover, the scheme allows accurate determination of the timing jitter between the electron beam and the seed laser, as well as a measure of the latter's effective pulse length in the FEL undulators. The scheme can be also provide an independent measure of the energy transferred from the electron beam to the FEL output radiation. We describe the proposed method as well as some experimental results obtained at the seeded FERMI FEL.