Learn English – Proverbs similar to “We’re not rich enough to buy cheap things”

The term that comes closest to what you're looking for is either trips or round trips.

A trip is a journey. A round trip is a journey that starts and ends in the same place. So if you start at home, travel to Paris, and then come back home, you have made a round trip to Paris.

In many cases, the "round" nature of a trip is implied. So the most common way of expressing what you're talking about would be:

You want to get a driving license? Oh, that's a pain. You'll have to make at least three trips.

The idea of multiple trips already, depending on context, carries some mild sense that the trips are a burden. If you use "round trips" instead, it emphasizes this:

You want to get a driving license? Oh, that's a pain. You'll have to make at least three round trips.

As best I can tell, this is the most idiomatic way to express what you're looking to express.

There are may synonyms out there for obsession in various forms - some can be perfectly fine in one scenario but carry a negative connotation in another, particularly when it comes to personal relationships.

For example, it it perfectly acceptable to be infatuated with a new hobby, but describing oneself as infatuated with a new girlfriend can come across quite badly.

One expression that comes to mind that covers all of the above scenarios without carrying a negative or overbearing connotation is 'really into'. I'm not sure if it fits into your idea of 'original and good-humoured', but consider the following substitutes to your original sentences.

1. Let's say you have a friend who is really into cats...
2. Another girlfriend is really into white-haired men...
3. A male friend is really into women who are petite...
4. Another male friend who is really into skiing...