I need to buy some rj45 connectors for the following cable. Unfortunately, I've never seen this type of rj45 cable. From which category comes it? Cat-4, Cat-5, ... Thanks
Without markings, it is actually impossible to say what type of cable this actually is, especially based on a couple of pictures. However, based on my experience, this looks like it could be a Cat5e or Cat6 specialty flat cable as it does indeed appear to be twisted pair (TP). The trick to identifying this as a form of UTP as opposed to a phone cable (which typically isn't TP) is to cut the cable cleanly a few times and examine the ends closely to verify the pairs are actually twisted.
Flat cables are often used in connecting entertainment equipment (TVs, streaming video players, IP speakers, etc) as you can maximize the space in any sort of wiremold used to hide the cables. The only ones I have seen have all been stranded cable meant to connect a device to the network infrastructure. I haven't personally ever seen a flat solid cable for use in infrastructure and have my suspicions they don't exist for a number of reasons.
We don't do product recommendations here, but if you do a web search for "8P8C RJ45 plug for flat ethernet cable" you should turn up a number of places you can get some. You may also be able to get by with ends that are made for round/oval cable if they crimp tightly enough.
Keep in mind that terminating your own cables (especially Cat6 or above) can be tricky and without a certification tester, you will never be assured that you meet any sort of standard. It is generally better to purchase pre-certified manufactured cables and use them instead.
That appears to be telephone (Category-3) cable. If you are using this for a phone system, then you are probably fine, but this cable should not be used for modern network cabling. The only currently recognized UTP cable categories are Category-3, Category-5e, Category-6, and Category-6a.
Your company should really hire a qualified cable installer to install a decent cabling plant.
FYI, that is not RJ-45 cabling (no such thing), and you don't want RJ-45 connectors. You want 8P8C connectors for UTP cabling.