That's a really good summary, although there are some inaccuracies.
Filling in a hotel form is by no means the same thing as registering one's residence with the authorities. It always has to be done in person.
Oh and you only have to state your religion if you are either Roman Catholic or Lutheran, any other faith or none is of no interest to the German tax office.
And the bit about 20 minutes being the longest reported wait at the Ausländerbehörde... Probably outdated and not a very thorough survey of all the alien departments in Germany. Now with the migrant crisis, they are all working with a skeleton staff and especially in big cities I have heard that applications are often simply not accepted on the same day but that the next available appointment is given, which can be several weeks or even months in the future.
Also, attitudes regarding residence cards seem to have changed in the last two years and a same day decision is only likely with good evidence of exercising treaty rights = working, not as a jobseeker. In case of applications within 90 days of arrival without evidence of working, health insurance, etc. the authorities now seem to tend to simply keep the application until 90 days have passed and then contact the applicant with a request for proof that the EU national is exercising treaty rights.
It is also interesting that the document claims that the Meldeamt is always in the same building as the Ausländeramt. This may be the case, especially in smaller towns, where all local authorities tend to be under one roof at the town hall but Berlin for instance has one huge alien department in the north of the city while there are numerous registration offices throughout the city with several in each municipality.
What else... no need to 'register' with a doctor or dentist. Simply find one, make an appointment and go. You are not obliged to go to the same one next time if you don't like the practice. Also, specialists like dermatologists, ophthalmologists, pediatricians, gynecologists, etc. have their own practices and there you can also simply make appointments and go, no need to be referred to a hospital and wait for an appointment letter for months on end. All of this of course, if you are working in Germany and have German health insurance.
This reminds me of something else.
As you are looking to bring your parents, they will not be eligible for free family health insurance the same way a spouse and children would be and will need their own. This could be very pricey.
Also, the part about being fine in daily life without German language skills, is not true as such. Yes, there are places that will be fine but this varies a lot - former East or West Germany? City or smaller town? Etc., etc.
I am not a regulated immigration advisor. I am offering an opinion and not advice.
I will definitely be looking to make genuine transactions which would produce invoices etc to support where the money has come from.