[noggin]

If I would use now an Apple TV behind the AV-Receiver:
1) Can I get HDR from Netflix / Prime? I guess yes

Yes - Netflix and Prime Video HDR content supports HDR10 - with some titles optionally also offering Dolby Vision support alongside HDR10.

2) Can I get HDR from iTunes? I guess not, because Apple uses Dolby Vision and I guess HDR and Dolby Vision are not compatible?

Yes - my understanding is that Apple also provide HDR10 versions of their content, not just Dolby Vision, as there are so many non-DV HDR TVs in use. If they only supported DV they would have a very small market to sell to.  Apple have committed to providing the bulk of their content in Dolby Vision, but that doesn't mean they only support Dolby Vision. (HDR10 is the de facto HDR standard and anyone who offers HDR will include HDR10 versions of their content)

3) What does "Lossy Atmos" exact mean, when streaming via the AV-Receiver? Is it still fully object based and only compressed (like FLAC/MP3)?

There are two versions of Atmos.

1. Dolby Digital Plus with Atmos - which is a lossy compressed audio format used by streaming services, TV companies (UHD sport in the UK has Atmos), and for secondary audio on some Blu-rays. This is not lossless but includes height extensions.
2. Dolby True HD with Atmos - which is a lossless audio format (just data compression, no audio components are removed) used on HD and UHD Blu-rays (often just for the main audio stream)

The Apple TV supports version 1. but not 2. of Atmos (so you get Dolby Atmos on streaming services, but don't get it from HD and UHD Blu-ray rips)

On an Apple TV Dolby True HD with or without Atmos is output in regular PCM 5.1/7.1 with lossless decoding of the regular 5.1/7.1 but no output of the Atmos height component stuff.  (Also I believe it only supports 48kHz audio - so if you have any of the relatively rare 96 or 192kHz stuff it will be downsampled)