Applies to Estonian tax residents.
Unemployment: unemployment insurance contributions are withheld from your payouts (1.6% on your side + 0.8% on Abillio's side), but Töötukassa's standard unemployment insurance benefit generally isn't available to people working under a käsundusleping the way it is for employees. A lower, means-tested unemployment allowance may be available if you've worked 180+ days in the prior 12 months and your income is low enough, but this is decided case by case.
Maternity/parental benefit: parental benefit (vanemahüvitis) is calculated from social-tax-liable income. Since Abillio pays social tax on your behalf, there's a real chance of qualifying, but minimum-threshold and continuity rules apply.
We recommend contacting Töötukassa or a tax advisor about your specific situation.