Those are perfectly normal things for young people who are trash at heart and have never received any parenting.

My SD does part of 1, does 2 a lot, does 3 mostly on weekends, does 6 when were not looking, does 7 mostly on the weekends, does 9 a lot lately, does 10 a lot lately and has done 11 on a few occasions lately. She is 12 right now. Her mom has a big part of why she does stuff like this. She can be a perfect kid, go to her mom's for 2 days and because her mom let her do all of this stuff for two days SD seems to forget that it's not allowed here.

Normal? Yes. Acceptable? NO.

Time to have a sit-down with DH and discuss house rules and consequences for breaking said rules.

Follow through with punishment for breaking the rules is key. Consistency is necessary. DAD needs to tell his princesses that their behavior is not going to be tolerated and that HE will dole out the punishment if the rules are broken, but you have that authority in his absence.

My BS15 does #1, #8 and since sexual topics are not taboo in my home some of #11.
#2 is normal for steps and bios and most teens, so I wouldn't care about that one. # 3 - I don't care about either. If they're home, there's no reason to be fully dressed. However to go outside they must be presentable.
4, 5, 6, 7, 9 and 10 are just bad parenting as far as I'm concerned. Kids LEARN that behavior from somewhere and they also test their boundaries. If a kid slams a door in my house I simply walk in, say in a calm voice "slam it again and it comes off the hinges." Problem solved.

They are normal for teenagers, but it's good if the parent disciplines them for at least some of it.

Burping and farting? That's disgusting. I really don't see what's funny about it. But then again, since there are even grown men who do it... I guess it's not something to stress about. They probably won't do it in front of a gf but just in the guys company so I suppose it's fine if they're all fine with it.

Constant fighting. Well of course, that happens. Hormonal, angry teens. What can they do if not fight?

Walking around in pajamas... Well, in the house it's okay. I do the same thing sometimes when I feel bad. If I'm sad, I'm lazy. And I just can't get myself to get dressed if I'm not going anywhere. And if they're staying in the house, why not? I don't think it's so bad. Kinda sloppy, but meh. Not worth a fight over it.

Door slamming? I never slammed a door. I don't see the point of it. It's not such a good release for anger, because if you do it more than one time, you're over doing it. And one time doesn't help me release anger. And it sounds terrible even to the one doing it. I didn't do it. And it's annoying and bratty. And it's damaging to the door and the wall around it. I wouldn't let them do it. If they kept it up, I'd make sure they pay if they F up the door or the wall. And they'd have to buy me earplugs. Then they can slam all they want. If they think it's worth it.

Cursing like a salior, well... I'd say it's "normal" for youth today, but I'd still try to teach them a better vocabulary. Or if not that, then for sure teach them where it's acceptable to curse, and where not.

Pushing around younger siblings is not okay. In most situations, NORMAL situations, an older sibling is someone to be protective and to be a role model. Now if there's a bit of sibling rivarly or fights, sure. But there's a big difference between normal pushing them around a bit, and actually being mean spirited to them. It's ok if they love eachother but get in a fight, but not if they actually are negative about eachother. You can't change how they feel, but you can stop them from hurting a sibling just from spite.

Never brushing hair, well... If they're guys, I guess it's normal. if they're girls, I'd be worried lol. Well, they should be taught basic hygene and that includes brushing the hair. But messy hair seems to be some kind of trend, so.. Just as with cussing, I'd teach them where it's acceptable to go with a bedhead, and when they have to comb it.

Taking and never asking? Sure, that's normal. They feel entitled to anything they find. I guess if they feel "at home", that's how it goes. I was like that too - if it's in OUR house, it's OUR, so I can use it. But if it's something mine, it's not our, it's MINE MINE MINE. I was a bad teen. Most are.

Just assuming they deserve everything? Oh yeah. Most teens. And a good share of adults, too.

Disrespecting father and SM? And mother, and aunt, and uncle, and teacher, and grandma, and any other poor thing that gets in contact with them. Pretty normal for teens to try that, but it should be stopped. As soon as they start with it. It's normal to be sassy, but it shouldn't be allowed. Even if they do not feel respect for someone, they should be civil.

Being overly blunt about sexual topics? Not only teens, but adults too. It's just our society where it's become acceptable, I guess. Not pleasant to hear if you're not one of them, but not much that can be done considering that everything is pretty sexual today.. And everyone is blunt about it.

the dad is afraid of being too harsh for fear of them not liking him.

I will never understand parents who let this determine how they parent. So, he wants to make sure they like him but obviously doesn't care if they respect him, and doesn't care that he's a crappy parent (and it shows).

When I was growing up, my parents didn't give a rat's ass if I liked them!

Sure, some of it's normal teenage stuff, but I wouldn't have done it around my parents.

Parents don't have to be harsh or mean to teach their children some manners and hygiene,
but if he has let them get away with this all along, trying to change anything will be met with resistance. They might respect him more in the long run, though.

He's going to have to get over the "I want them to like me" thing. They are not puppies.

I've got an 11dd, 13ds, 15dd and ss14. Here's my take.

1. Burping and farting and laughing at the "big ones".-No, not so much. I have a very sensitive sense of smell and have so taught these kids at an early age that it is gross and nasty to fart or burp anywhere near me and you will likely be sent to your room if its a "big one".
2. Constant fighting-no, not so much with my bios-if you want to throw ss in the mix then yes, every day all day long-but that's just him and I would say he is not normal in any way shape or form.
3. Walking around in pajamas all day everyday no matter the place. Again, no. My kids might wear pj's around the house til noon or something-but they do go out in public that way and they change into regular clothes at some point. My ds sleeps in basketball shorts.
4. Door slamming-nope.
5. cursing like a sailor. Nope. Dont allow my children to curse in front of me-i'm not naive enough to think it doesnt occur away from me, but whatever. I have found myself, of late, allowing the word "freaking" which used to be a huge pet peeve of mine. I must be getting soft in my old age.
6. Pushing around younger siblings-no, this would really piss me off-again unless we are talking ss-I am answering these for the most part as if he's not included as I said he is simply not normal in anyway.
7. Never brushing or keeping up with hair-no. Even my ds13 makes sure his hair is always brushed before leaving the house. He may not brush it if hes not immediately going anywhere that morning.
8. Taking and never asking-I'm not sure exactly what you are referring to here. They do help themselves to snacks and such which at times they overdo it and that annoys me. My dd11 also likes to help herself to my perfume, makeup, etc-but generally they ask for anything else.
9. Just assuming they deserve everything-if they begin to assume this I put them in place immediately-my ds13 has a problem with this sometimes.
10. Disrespecting father and SM-occassinal, minor disrespect-mostly my beefs with the kids are that they are messy and dont like to clean! LOL!
11. being overly blunt about sexual topics-I will have to say a yes to this one. Not really my 11 year old-because she's 11-but definitely my 15 year old, and at times my 13 old. I agree with what someone else says-this just seems to be the norm nowadays-I certainly want my kids to be comfortable talking to me about sex, but I have to admit I die inside a little everytime I hear my daughter talking about so and so giving so and so a blow job. I dont believe, even to this day, that I have ever uttered the words "blow job" to my mom and dad. Although, my mom and dad did ask my dd15 what the whistle song was about one day. She told them it was about a coach! LOL!