That's one FUBAR nid. I can tell you this, your line is unbalanced.
To expand a little on nunya somewhat cryptic post you have a NID that can be configured for one or two phone lines. Currently only one line is installed.
You indicated the black wire off the the right is the drop into the house. There are four other cables. One of which should be ground, usually Grey but I don't know if that is a regional thing.
That leaves three inside cables so one would expect 3 Red (Ring) wires and 3 Green (Tip) wires connected to the customer premise equipment (CPE) terminals. I only see 5 wires.
Phone lines are balanced relative to ground to prevent hum. Screwed up inside wiring is has to be really bad to mess up voice but DSL is much more sensitive to unbalance.
So the first step is to fix your existing inside wiring. A splitter is not going to help resolve and unbalanced line.
I agree Cat5e is overkill but it makes since to use Cat5e for phone wiring since it is the same prices at Cat3 and allows the possibility of converting phone line to Ethernet drop in the future.
If your inside wiring is twisted pair of any flavor there is no sense in replacing it. Judging from your picture house is wired with quad-four cable that is not twisted. That is vulnerable to crosstalk but is not an issue in your case since you only have one line.
Priority should be: 1) Check stats at NID compared to normal DSL modem location 2) With phone connected to NID test jack evaluate voice quality 3) Fix unbalanced pair 3) If DSL stats are better with modem connected to NID install a splitter with dedicated run to modem location using twisted pair cable. 4) If after doing all that and modem stats are still better at the NID test jack than normal location disconnect all non-DSL equipment from line. If stats are still bad replace phone wiring. It is very unlikely you will need to do step 4.
I think I see the "issue". It looks like somebody broke the ring wire off of the terminal and just wrapped it around the screw rather than replacing the module. -- If someone refers to herself / himself as a "guru", they probably aren't.