Hi and welcome to the forum.

I suppose one of the reasons it's hard to find estimated moving costs is that there are so many variables. Moving furniture depends to a large extent on how much stuff you are going to move, how you want to move it, and whether or not you want to attempt to move it without buying shipping insurance. Then, too, the insurance will depend on how much value is in the items you're shipping.

Moving a pet will depend on how you do it, what sort of pet, etc.

I don't understand what you mean about "cleaning carpets in the place we end up renting" - I suppose it depends on what sort of place you end up renting and whether or not you're obligated to clean the carpets. But I can tell you that US style wall to wall carpeting is not nearly as common in Europe as it is in the US.

Language tutorial again depends on how you want to do it - Berlitz or private one-on-one tutoring or just buying a CD course to play in your car. Your level of language learning will have a big effect on the ultimate cost, too.

Then there are the hidden costs. Things like replacing small appliances that aren't worth moving over (unless you want to buy many, many transformers to run 110V items on European 220/240V mains), or paying VAT or customs on items you ship over that incur those charges for whatever reason. Also agent fees for finding a rental to live in, plus deposits on a place to live, which can total 2 to 3 months' rent you have to pay up front.

Best idea might be to list out all the items you expect as part of the cost of relocation and run it by us here in the forum. I'm sure we'll have a few "new" things to add. The only way to get a decent estimate for your costs will be to go through and get separate estimates for each item, based on your own circumstances and requirements.

Coming from the US, there is also the issue of what moving costs are and aren't deductible on your US taxes (depending on the reason for your move - if it's job related, some of the costs will be deductible). And don't forget the various fees required to apply for your visas (filing fees, medical exams, private expat health insurance unless you'll be covered by the national health system when you arrive, etc.). It's not an easy question to answer.
Cheers,
Bev