WiFi – Difference Between Ad-Hoc and WiFi Hotspots

1.) The Microchip wifi Beacon announces the network, I assume the BSSID is randomly assigned in IBSS / Ad Hoc mode.

To some degree, this is true. For clarity, from IEEE-802.11-2012 section 10.1.4.1:

When a STA starts a BSS, that STA shall determine the BSSID of the BSS. If the BSSType indicates an infrastructure BSS, then the STA shall start an infrastructure BSS and the BSSID shall be equal to the STA’s dot11StationID. The value of the BSSID shall remain unchanged, even if the value of dot11StationID is changed after the completion of the MLME-START.request primitive. If the BSSType indicates an IBSS, the STA shall start an IBSS, and the BSSID shall be an individual locally administered IEEE MAC address as defined in 9.2 of IEEE Std 802-2001. The remaining 46 bits of that MAC address shall be a number selected in a manner that minimizes the probability of STAs generating the same number, even when those STAs are subjected to the same initial conditions. The value SSID parameter shall be used as the SSID of the new BSS. It is important that designers recognize the need for statistical independence among the random number streams among STAs.

So, the first STA to start in the IBSS should generate the BSSID, however further STA's that join the IBSS should adopt this value.

2.b) The iPhone6 sends a probe request to the randomly assigned BSSID and never receives a probe response, therefore not knowing that the Microchip can only listen on 1 / 2 Mbit / s and starts talking at 12 Mbit / s in further conversation, which obviously doesn't work.

I will start by noting that there isn't a single probe response in this capture. This leads me to believe that there is some sort of problem with how this capture was obtained. As such, there is no way to determine if the Microchip device has responded with a probe response or not.

However, we can assume that a probe response has been sent and recevied at some point because it appears your iPhone6 has joined the IBSS. Take a look at the beacon frames at 19.85 seconds into the capture. You now see both the Microchip and the iPhone6 sending beacon frames for "Anova 1" with the same BSSID. Since they have synchronized the BSSID, this would indicate they have both become part of the same IBSS.

The question now is which of the two wifi firmwares behaves not according to the 802.11-2012 standard?

Based on the evidence at hand, and technically speaking, they both appear to be adhering to the standard. We would need a better capture to make any further determinations.

I'm investigating an issue with an iPhone controllable hardware, which operates in IBSS / Ad Hoc mode. Since the hardware generation of iPhone6 & Co the iDevices can't connect to the hardware anymore, which creates the wifi network with a deprecated Microchip 802.11 b listening only to 1 / 2 Mbit / s.

It looks like the IBSS is established. You need to start looking at why the two are not actually communicating.

Can we use CSMA/CA (Carrier Sense Multiple Access / Collision Avoidance) on wired networks?

In theory, yes.

If yes, then is there any protocol that uses CSMA/CA on wired network?

Nothing in use today

If no, why?

I was guessing, it must be technically possible to use CSMA/CA on wired network, but most of them use CSMA/CD, because sending signal and then striving to detect any collision is faster than first ensuring collision will not occur and then sending signal. I am correct with this? Or is there any other reason?

Sounds reasonable to me. but to be sure, you'd have to ask the people who invented Ethernet (Bob Metcalfe) that question. Remember that Ethernet and other protocols went through several stages of development and refinement before becoming what it is today.