When you start looking at the OSI model, things can become very complicated.
Different level 2 protocols exist because at the time, they were better for different things (still true to some extent).
Level 1 "devices" exist as they are needed for different environments, for example IEEE 802.3 represents Ethernet and IEEE 802.11 represents WIFI, both of which are layer 1 physical layer.
Taking this a bit further, 802.11 and 802.3 whilst not compatible with each other on the physical layer, they are cross compatible further on in the model and all they require is some sort of device to make them cross compatible (e.g. a level 2 switch), therefore, they work fine through a router.
Basically put, level 3 in most environments is networking as we know it - IPv4/6 addresses, ICMP features such as ping, security through IPSec and more. But, it doesn't have to be.
It is possible to have a completely different networking infrastructure environment with your own level 3 specification, this is most commonly seen in industrial controls and similar where there are very specialised needs, these devices may use a common level 1 or level 2 feature, but, may have a completely different level 3 stack meaning that routing between the devices would be impossible.
I am sorry, but, this is a very advanced topic to try to explain, I hope I have helped, but, I fear I haven't - feel free to ask follow up questions and I will do my best to answer.