At the gate - the risers (height of step) are all supposed to be the same, the rise beteeen the top conc. step and road level is not the same as the other two risers.
Cast lintels don't come free, maybe shutter one or more new path gravel retaining steps, possibly to take any slope out of the path. Make sure that you lose some rebar in new conc. steps or they'll snap, especially if they're long, don't put rebar close to surface of concrete (rebar should have 50min cover of conc, see images of the ends of conc. lintels)
There are min and max recommended riser dims (and also goings dims).
You can make steps down each side of door out of conc. or blockwork, in either case the riser could be faced with (engineering/frost proof) bricks and there are plenty of natural stone/slate finish type conc. paving slabs available for the top surfaces.
Also, look at falls info re step surfaces where steps are outside, to allow water to drain.
A drill on hammer action is a makeshift way to briefly vibrate shuttering and get any air up out of the mix.