In my experience, TekSystems (an IT hiring agency) have proven to be a waste of time. Even if you manage to secure a job through them, be prepared to sacrifice a significant portion (10-30%) of your potential salary, as they'll deduct your hourly/salary pay as a finding/employment fee. I'm not sure if this is common practice with other recruitment companies but I find it to be very scummy
This is not customary. In fact I've never heard of it for placements. A broker for consulting work might take a finder's fee, but never for regular employment.
Way back when, like in the 1950s and 60s, employment agencies might take a percentage. The shift to more contract work, where the percentage is baked into the billed rate vs. what they pay, has ended this.