I'm not going to straight up tell you the answer, as you wouldn't learn very much from it, but here are a few hints as to how you could go about things – see how you get on and ask again if you're stuck

BaCa(CO3)2; Mr = 297.4 g mol^-1
Avogadro constant = 6.02 × 10^23 mol^-1
(a) Percentage by mass of oxygen
– To work this out, you'll need to use the Mr of alstonite, and the Ar of oxygen (find it on a periodic table). Work out how many oxygen atoms are in 1 unit of alstonite, the relative mass of all these oxygens, and then do a percentage calculation to find the % by mass.
(b) Total number of ions in one mole of alstonite
– You know the compound is a salt (i.e. ionic), and by looking at the formula you can work out how many ions are in one unit of alstonite. From the Avogadro constant, you know that there are 6.02 × 10^23 "particles" in one mole of substance, i.e. one mole of alstonite has 6.02 × 10^23 BaCa(CO3)2 units. A bit of adding and multiplying and you can work out how many ions are in one mole of the salt.
(c) Moles of HCl to react with one mole of alstonite
– First of all, what is the reaction between HCl and BaCa(CO3)2?
– Once you know what is happening, write an equation for the reaction, and balance it (hint: keep the "big number" in front of the BaCa(CO3)2 as 1). Then just read off your equation to find the moles of HCl reacting with BaCa(CO3)2.