Do you mention the food in a dinner invitation?

Ha! Well, I always have enough "neutral" food on hand so no one goes hungry. Salad, rice, potatoes, bread etc. and the dessert course is always meatless. I try to make the appetizer meatless too. Flatbread pizzas etc.

I just usually ask them over, then figure out what I feel like making for then later on...

Ha ha, #4! People with food issues! I usually liek it really spicy, so I can leave the peppers on the side in most dishes for the really wimpy. I've had to deal with some cheese-haters in the past, but I didn't say anything when I served the quiche and they gobbled it up!

I'd just invite them over for dinner, and ask whether there's anything thye can't/won't eat.

I don't normally decide what I'm going to serve until a few hours before. And even then I might change it if something dorsn't work out for example.

I would just invite people over, but thinking about the exceptions seem to be when I invite people for a curry or a roast, then I say do you want to come over for a curry/roast. Maybe because the style of eating for those meals isn't like a fancy dinner... when I do curries is very informal, loads of people and big pots on the table and a roast is usually a load of hungover people on a Sunday stuffing their faces and drinking lots of red wine for hair of the dog.

I never ask people about allergies etc, they need to let me know if its that important/serious for them.

I usually invite just saying "for dinner", and I see the food being served as a part of surprise. But, then, almost without exceptions, my guests are people that I know well.
Although, a couple of times, it happened that a friend sitting at the table, suddenly uttered "no thank you, I won't be eating". (Me: "I beg your pardon!?").
That happened with two newly converted vegetarians. One of them is now a born again omnivore.

I usually mention at least the main course we'll be having.

I'd just ask them if there are special dietary requirements at all.

I always clearly state the arrival time for pre-dinner drinks. Latecomers have to choose from a list of bizarre and humiliating public forfeits. I list the nibbles and the aperitifs. A seating plan is de rigeur both for our retro-chic conversation pit and at the dining table. A few days ahead of time I email out a powerpoint presentation introducing the guests to the menu and preparation methods, specifying the exact source of produce together with its carbon footprint and the airmiles involved. I find a set of cue cards helps the prandial conversation along. I also video the occasion in case of any social gaffes, embarrassing revelations or split infinitives.

istanbull, istanbull. How can you do that?

No dress code? No pre-dinner questionnaire to help decide the seating plan and the menu? Where's the GPS coordinates or your front door? The floor plan so they know how to find the toilet? What about when it's time to go home? Do you sound a gong or just have a live orchestra play "Good Night Ladies"?