I don’t know much about cabling and need some help identifying what this is.
There this port that has a phone and a computer icon near where the fibre/coax entries are.

And in one of my room there’s this dual port jack with those cables :

No, but what you have might be usable.
The jacks, at least the ones where you show the back with the screw terminals, but probably the other ones as well, are standard 4-wire phone jacks, which can handle one or two ordinary phone lines (POTS) or many (but not all) traditional phone systems, except for VOIP. VOIP uses regular Ethernet networks, which is what you want but don't have.
My hunch is the computer symbol dates back to old modem days. In ye olden times, computers in a typical home or small business were not networked but many would have a modem connected to an ordinary phone line to call up an internet service provider or, in even older times, Compuserve, AOL, bulletin board systems or proprietary systems such as minicomputers or mainframes for shared databases or accounting systems.
The possible good news is that these are 4-pair cables, which are what you need for Ethernet. The likely bad news is that they are probably Category 3 (Cat 3) cables. Cat 3 is only rated for, and reliable at, 10 Mbps, which is marginal for modern networks, video on the internet, etc. Zoom and similar platforms typically specify 3 Mbps - 4 Mbps for a single video user. 10 Mbps in theory should be enough for 2 simultaneous users or 1 plus miscellaneous email, web browsing, etc. However, I have seen compatibility issues with newer switches and equipment with older 10 Mbps networks. In theory most equipment is backwards compatible. But reality is not always the same as theory.
Cat 5 can handle up to 100 Mbps, which is good enough for typical uses. Cat 5e can handle up to 1 Gbps (1,000 Mbps) and has been standard for many years. If the cables are Cat 3 then don't even try to use them for modern (100 Mbps and up) Ethernet. If the cables are Cat 5e or above then you're all set (maybe...see below) and if they are Cat 5 then they probably are usable for things that don't really need more than 100 Mbps - e.g., OK for a computer or two web browsing, Zoom, etc. but not for an in-house network with serious data transfer needs.
If the cables are not good enough, you may be able to use the old cables to help pull new cables through the walls. That depends on whether the old cables are stapled or otherwise secured in place, which is likely if the old cables were installed before the walls were finished but unlikely if the old cables were themselves an addition to an already existing building.
Adding Ethernet jacks to existing cables is a relatively simple process. There are special tools required to do it "right", but they are not expensive and not hard to learn to use.
But there is one more possible problem: topology
Traditional phone lines, including fax and modem lines, could be daisy-chained from one location to the next. Ethernet doesn't work that way. Well, usually it doesn't - within certain constraints you could use Ethernet switches as a way to bridge pairs of cables. But generally speaking Ethernet is wired in a star topology - lots of cables that start at one location (which is where you place a nice big switch, and possibly your router, though not necessarily) with each one going to a jack in a different room. Your pictures show a typical daisy-chained configuration. So even if the cables are Cat 5 or above, you can likely, practically speaking, only connect one location as a regular Ethernet connection, without quite a bit of extra equipment.
Digital Subscriber Line/Loop (DSL) is a way to get internet off plain old telephone service. Also known as ADSL, ADSL2, VDSL, VDSL2, etc.
The sound of the DSL traffic would be very screechy to the telephone user, so the filter was put on the "phone" side to remove all the high frequency DSL signals. Every phone needs such a splitter or filter.
It is not ethernet, however the cables in the wall look reasonably modern, like Cat3 or Cat5, might be reusable by putting Ethernet faceplates here. Ethernet speed would likely be limited depending on wire performance. A lot of that old stuff exceeds its spec enough you can still get workable speed out of it.
Ethernet isn't designed to be wired in daisy-chain style, but it can be by over-using hubs and switches. The topology might force you to put a hub or switch at every outlet. But I don't gather you plan to use more than 3 of them, so that won't be so bad. Note that 10Mbit and 100Mbit ethernet only require 2 pair (4 wires). Thus on common 4-pair cables, you can actually squeeze two separate Ethernet routes (out and back).
The second one is just a 2-socket cover plate. Nothing special going on there.
Not likely.
The wiring in your last 3 pictures is likely Cat5, being used as telephone wire (one pair in use) and the fact that two wires are seen here means they daisy-chain from port to port (as opposed to home-runs which are necessary for network cabling).
Additionally, none of the ports look wide enough to be RJ-45 (the network standard with 8 pins) these are probably RJ-11 (telephone standard with 2, 4, or 6 pins). The back of the plate has 4 contacts, only 2 of which are in use.
If you're not using landline telephone you can see about using these cables to pull real network cable (Cat5e or Cat6 are the most popular) into these locations and replace the wall plate with a real RJ45 network jack to use for computer networking. As-is, you probably won't get much mileage at all out of them.