Depends on the work, honestly. For a job that requires contact with customers during business hours, or trading on a stock exchange or other market with limited opening hours, or international contacts with particular time zones, it makes sense that you don't want people working whatever hours they like.
In my job, everyone who is working that (half) day is required to be in the office (or out on work-related things) between, iirc, 9:30 to 11:30 am, and 2 to 4 pm. The rest is up to you, as long as you reach the required amount of hours per day (and the office does have opening and closing hours at 7 am and 8 pm respectively). Which is fair enough as far as hours go - just annoying that in extremely calm periods they don't let us leave earlier.
This is indeed silly - arguably even counterproductive, as people taking very long holidays do saddle their colleagues with lots of extra work, but less than people taking lots of short holidays, since then the colleagues have to do an extra effort to take over the absent person's work every single time, as opposed to making that effort just once and then handling it for four whole weeks. On the other hand, for the kind of work where it really is not feasible or acceptable towards the customer to have a substitute handle it, justifying an absence of more than two weeks of the responsible person does become a little hard.
That does seem normal enough to me... even leaving at 2:30 pm would be rather bizarre unless you had started work unusually early for some reason.
This, eh, depends on how strictly the rule is enforced. In my company (which, admittedly, lacks a real HR department despite having over a hundred people in the office), we have similar rules, but they are pretty much ignored except when their violation results in real harm to the company, or real trouble for the colleagues who have to cover.
In that case, yeah, you're justified in being demoralized - regardless of whether the rules themselves are really that harsh or not, it is clearly a tightening of the rules that only makes sense when there is a real need for it.
Not really, but as to whether it's smart to pick a new fight...
That sucks. Perhaps you can still negotiate longer holidays if you arrange them long enough in advance? Depends again on how strict enforcement will be, I guess.