The ATLAS collaboration has performed several measurements in special data sets with low LHC beam currents, recorded at a center-of-mass energy of 13 TeV: Measurements of the inclusive charged-particle multiplicity and its dependence on transverse momentum and pseudorapidity are presented and compared with predictions of various MC generators. The collaboration has also performed measurements of the number and transverse-momentum sum of charged particles as a function of properties of the leading high $p_T$ track in the event at a center-of-mass energy of 13 TeV. The results are compared to predictions of several MC generators. In addition, the total inelastic proton-proton cross section and the diffractive part of the inelastic cross section was measured, using special forward scintillators or the calorimeters. The latter result completes the measurement of the elastic pp cross section in a dedicated run with high beta* optics at 8 TeV centre-of-mass energy with the ALFA Roman Pot detector. From the extrapolation of the differential elastic cross section to t=0, using the optical theorem, the total cross section is extracted with the luminosity-dependent method with high precision. Furthermore, the nuclear slope of the elastic t-spectrum and the total elastic and inelastic cross sections are determined. Finally, the collaboration has studied the hard double parton interactions (DPI) in events with 4 hadronic jets and translated into a measurement of the effective DPI cross section. Several DPI-sensitive variables are unfolded to particle level and compared to predictions of different MC models.