If you're new — a catechumen, an inquirer, a new convert, or fasting for the first time — read this before anything else here.
Before you take on the fast, talk to your priest or spiritual father. He may adjust it for you — and may allow things outside of how the Church generally fasts. That isn't a lack of rigour; it's how the Church has always fasted. The fast is kept through obedience and relationship, not by a perfect score and legalism.
You will slip. Everyone does. A broken fast isn't a catastrophe — just get up and keep going. The goal is to exercise control over your passions, to be humbled, to soften your heart, not to achieve a clean record.
We fast to pray more, give more, and lean on God more — to loosen our grip on our own will. It's not a diet, not a competition, not a way to prove you belong. The Fathers warn against fasting from food while feasting on judgment of others. Pray more. Give more. Serve more. Lean on God more.
Faithful Orthodox Christians disagree about what "oil" and "wine" mean when they're prohibited. Some say only wine, some say all alcohol, since wine was the everyday drink they had. Some say only olive oil, some say every oil, including seed oils in processed food. Look hard enough and you'll find a saint or canon for any position. It's tempting to settle it yourself. DO NOT DO THAT.
You grow into the Orthodox phronema (the Orthodox mind) by being in obedience to your priest or spiritual father. That humbles you. So does the fast he gives you. You're not the judge here, and that's a relief. Ask him, then get back to the fast.
Feast or Fast tells you what the calendar says. It can't know you, your health, or your parish. Let it guide you — let your priest, and the life of your parish, form you.