Yes, probably, Family - dogs are hugely popular.
Health insurance here is a legal obligation and if you're employed, your employer must provide it. Unless you earn loads of money you have a state-funded health insurance provider, you pay 7.5% of your salary towards this and your employer pays the same amount on top of your salary. But it doesn't matter whether you're paying 7.5% of €20k a year or 7.5% of €100k a year, the service is exactly the same. There is a top limit on how much it can cost which is nearly €5k a month. If you earn more than €60k a year (ish) you can choose to have private insurance instead which does get you slightly nicer treatment - nicer rooms, shorter waiting times, you will tend to get the head surgeon rather than just any surgeon at the hospital, etc. But not a huge difference as I understand it. The main difference is that with private insurance you pay upfront and get the money reimbursed. Whereas with state health insurance, it's free at the point of use (there are some token charges for prescriptions, ambulance, hospital stay, and things like physiotherapy.)
Spouses earning less than €450 per month and dependent children can be insured under the main wage-earner for no extra cost. Unemployed people are insured by the state funded health insurance (I think) for free. Students, I believe the same. If you're self employed you have to pay the whole 15% yourself, although there's a minimum fee, which is about €180 a month, so being self-employed on a low income can be tricky. If you earn less than €450 a month self-employed, you can just be on your spouse's insurance as a dependent, though. I don't know what happens if you're single. I guess if you're single you need to be earning more than €450 to survive anyway!
I don't think that health insurance is expensive at all. I just consider it another kind of tax.