How do you think they would verify or sanction an invalid ballot? Given that voting is secret and therefore there's logically no personal information on the ballot, this would be rather tricky - or extremely worrisome for democracy. ;) So no, it's definitely not illegal in any somewhat democratic nation. And yes, most countries do count invalid votes separately. This can be an important indicator that something went wrong. Eg if suddenly all districts report much higher numbers of invalid ballots, something might have gone wrong in the counting process or just the ballot design might be too confusing. Definitely worth looking into, though. And if a single district shows an unusual count of invalid ballots compared to others, that also is worth looking into.

Many that intentionally vote invalid claim to do so to show their frustration with all party options. However, this hurts democracy. Even if do not love or even like any of the parties/candidates, you still should vote.

Vote for the "least of the bad". A vote for a democratic candidate that has a boring mix of policies planned that you don't fully support is still a lot better than anything on the other end of the spectrum, with radical extremists working to undermine society or democracy itself. By voting invalid, your missing vote ends up being "shared" by everyone, and I'm certain there's some on the list that you really don't want to even have the tiniest shred of your vote.