In Australia, men and women regularly socialise with members of the opposite sex and develop friendships that don't involve romantic feelings. If someone invites you for coffee, or asks you to attend a social event with them, it doesn't necessarily mean they're trying to start a romantic relationship. They may just want to be friends!
People who know each other well mostly meet up in informal groups to socialise, and these groups can include both friends and romantic partners. However, they can also go on dates with their romantic partners.
Both men and women can invite people on dates. It's not usual for a couple to be chaperoned or accompanied by an older person on a date, but frequently, couples going on their first date will go out with a group of friends, or meet at a location where their friends will be, such as a coffee shop, cinema or pub. This tends to make the date a lot less awkward than it might otherwise be! If someone asks you to go out, it's okay to ask if any of their friends will be there, or if your friends are welcome to come along. Your date may also invite you home at the end of the evening for a coffee or a drink, but you don't have to accept if you don't feel comfortable, or think it's inappropriate. If you don't want to go to their home but do want to see them again, this is a great opportunity to arrange another date instead, though!
Couples mostly share the cost of meals or activities when they go out, but if it's a special occasion, sometimes one person will 'treat' the other by paying for everything. If this happens, the other person usually reciprocates by paying for another date on a later occasion. It's never okay for someone to tell you that you 'owe' them sex because they paid for a date.
Relationships can vary from casual friendships to romantic attachments that include deep emotional and/or sexual involvement. In every kind of relationship, you have the right to decide whether you want to have any sort of sexual contact with your partner. Agreeing to participate in a sexual activity is known as consent, and it applies to everything, from holding hands and kissing to sexual intercourse. Both you and your partner need to give active consent for any sort of sexual activity, and early in a relationship, it's best if this consent is verbal so that everyone knows where they stand. Your partner should always respect your 'no', and you theirs - if you don't give consent and your partner continues to push sexual activity on you anyway, they are committing sexual assault.
There are really very few set customs or rules in Australia about intimate relationships - same-sex relationships and couples living together without being married are both legal and socially accepted. What rules there are focus on treating your partner with respect and as an equal. Most people draw on their own social, religious, cultural and individual beliefs and values to decide how to handle their friendships and romantic relationships, but they don't expect that people from other backgrounds will do things the same way. Because of this, it's a good idea to be clear about your own expectations of relationships and dating when you meet a new partner, and to be open and honest about them. That way everybody can make the best choices for themselves.