It depends on what you want to sew. If you want to sew only knit casual wear, a serger is fine. Anything else, you also need a sewing machine. Any but the most basic sewing machine can do anything you do on a serger (including cutting and sewing at the same time if you buy the right attachment), but not necessarily as quickly and easily.

Both. They do different things. Best comparison I can give you is to say “I have a stock pot, do I really need a wok?”

A serger (overlocker) makes finishing seams really fast. You need a sewing machine, but an overlocker is a helpful extra. Look out for a secondhand Bernina or Bernette machine, they’re wonderful overlockers.

If you started with a serger I would recommend you also get a sewing machine. If you started with a sewing machine I would say a serger will make many things more convenient but you can get by with just a sewing machine. If you are wanting a sewing machine that can do lots of different projects, get a "Heavy Duty" one rather than one with lots of computerized features. You'll be happier long term with a strong motor than endless decorative stitches. Refurbished machines can be a great deal.

Yes you need both.

A sewing machine is definitely a must. Having both is absolutely acceptable

Yes. IF you are sewing garments, there are some seams that cannot be serged.

Don’t get a serger until you have some experience sewing, garment construction, fabric choices, fitting expertise, etc. Sergers typically cost more than sewing machines and they are very tricky. Experience is important.

I like having both, but many things can be made with just a serger.

You do! You need a regular machine for button holes, zips etc