I would be surprised if you have a tyre problem. New tyres can sit on the shelf for up to three years before they are sold as being new.
If me, I would put about 40 psi in them, drive around for a few miles to warm them up, that few miles should sort out any irregularities. Then put the correct tyre psi, preferably when they are cold.
Correct pressures will be on a sticker on the driver's side door pillar, but am sure you already know that...????
Engine oil, I would change it, manufacturers usually quote a mileage OR a 6 months time period, better safe than sorry.
As for the other stuff, can't think of anything to worry about..????