Working in Switzerland, living in Austria: taxed in both countries, with a credit
There is no frontier-worker rule between Switzerland and Austria. Switzerland deducts its ordinary withholding tax (tariffs A, B, C and H, no cap) from the pay for days worked in Switzerland, and Austria taxes your whole salary in the income-tax assessment, crediting the Swiss tax up to the Austrian tax on that income — in effect you pay the higher of the two. Home-office days in Austria are taxed only in Austria.
The Austrian assessment (forms L1i and L17) deducts the Swiss AHV/IV/EO, unemployment and BVG contributions and your health premium as Werbungskosten, plus the Pendlerpauschale and Pendlereuro if you qualify, and taxes the 13th salary within the annual sixth at the reduced rate for Sonderzahlungen. Not confirmed: whether the extra-mandatory part of the BVG is fully deductible.
Health insurance: within three months you choose between Swiss KVG and Austrian cover; enter the premium of your choice — none is assumed. The Swiss withholding tax is approximated with the ordinary tax of the work commune and can differ from the cantonal tables; for a canton the calculator does not model, enter your withholding rate.