I"m going to try to answer your questions in reverse order because my answer will probably make more sense that way.
How hard is taking care of first day born kitten?
It's hard. It's a pain in the you-know-what.
New-born kittens need to be bottle-fed every 4 to 6 hours with a suitable milk-replacement formula - no, not 'normal' cow's milk as that doesn't have the right nutrients for a kitten and could actually do more harm than good. There are kitten milk powders (KMR for example), but they're not cheap.
Then once you've fed them, you need to "poop" them. If they were with their mother then she would lick their behinds to stimulate the reflex which makes them poop and/or pee. Ok - so even though the actual licking bit isn't critical, you still need to do something similar like gently rub those bits with a warm damp cloth while waiting for the kitten to do its business onto said cloth.
Now remember - you're doing this 4 or 5 times a day for at least a few weeks.
Should I take her kitten in the day they are born, or should I wait until
they open their eyes?
So, following on from above: No you shouldn't take the kitten the day they're born, because their mother is far better equipped than you are to feed and care for new-born kittens.
In addition to this, your description of your friend's situation where their cat is having up to 3 litters a year for some number of years running, leads me to believe that these kittens are very likely not going to be in the best of health to start with and there is a very high chance that some (or even all) of the litter may die despite your/your-friend/mommy-cat's best efforts.
The longer you wait, the higher the chance that any genetic defects or general health problems will have shown themselves, giving you a better chance to choose a more healthy kitten from the litter.
Trust me on this - if you have even the tiniest shred of compassion in you, you really do not want to be holding a kitten as it dies if you don't have to.
Leaving the kittens together and with their mom for a while also serves another purpose - it helps to teach them how to socialize together and develop healthier personalities.
Kittens are naturally very playful & sociable and they learn & grow far better together than they do alone.
With this in mind, I'd strongly recommend that you wait even longer then when they start to open their eyes (typically 7-10 days). You really want to wait until they're comfortable eating solid(ish) food on their own and don't need to rely on mom's milk, and this is really 4 weeks to a month at the absolute earliest, preferably longer.
Is it cruel or bad taking her kittens?
Well - that depends.
In my opinion, taking them too early is cruel and unnecessary.
But in the long run they'd leave their mother on their own anyway, so it comes down to when & how you take the kittens.
When thinking about the kitten, you need to know that you are able to properly look after the kitten at the age you take it. Take it early and you need to be prepared for bottle-feeding & pooping multiple times a day, and (particularly if it's alone) you might end up raising a cat which isn't really well-adjusted and might show odd behavior issues sooner or later.
When thinking about the mom, it's probably better for her to not take the entire litter all at once, since not only is she still producing milk for them and she'll become very uncomfortable if there are no kittens to drink it, but she will also still have all of the hormones & instincts driving her to look after her kittens - so letting them grow up a little and then taking one or 2 at a time over the space of a couple of weeks will leave her less distressed.
I've been assisting with cat rescue volunteer groups for a few years and there's one more thing which you haven't asked, but I feel strongly about.
Please encourage your friend to get their cat spayed.
It is not good or healthy for a cat to be giving birth to 2 or 3 litters of kittens year after year.
Her life will be significantly shortened and stressful as it is now, and we don't need any more stray/feral/neglected kittens than we already have.