I'm thinking about bacterial/wild yeast contamination etc.... Or will just washing them under the tap be suffice?
Also can I use the cores?
As you are making hard cider you just need to juice the apples then add your choosen yeast to the juice. You don't need to boil or even wash them, but you can. Many traditional ciders are fermented with the yeasts and bacteria found on the skins of the apples with no additional yeasts added.
Yes, you can mash the whole lot up cores/skin and all if you want, I would juice or press them personally.
I don't know what apples you have but if you only have sweet eating apples I would advise adding some cooled black tea to up the tannin levels or your cider can sometimes lack body. Cider apples are far more bitter than eaters and have far higher levels of tannis.
If you were to use them in a beer mash, you should heat them to >70C to ensure that you gelitenise the starches and can extra all their sugars in the grain mash.
If you make cider, you do not need to mash.
As explained by a French cider farmer I visited once, crush your apples and let them turn brown, then press them for juice. Also, try to make a mix of apples, do not only use sweet apples, also try to add sour and bitter apples.
I do recommend at least pasteurizing the juice of from fresh pressed apples. Bring the juice to 160°F for a few minutes, then cool to 65°F before pitching yeast.
Boiling the cider can be done but this changes the flavor and boils off water increasing sugars.
Not all cider makers pasteurize or boil. But Not doing so will have other microbes working along side your yeast and doesn't always have good results. While others have amazing results from wild or spontaneous fermentation. It really is a gamble untill you have the skills to insure your pitched culture dominates.
Yes it's ok to use the Apple cores if you press the apples. Just 1/4 them and press. You shouldn't use the cores if you use a juicer as it may cut or break seeds allowing unwanted chemicals into the juice. (Cyanide)