I add test points to a majority of the boards I work on - unless the client specifies otherwise. I won't add test point for every net, but power and ground nets definitely get a test point. When we get a batch of boards back from the fab house, I grab the DMM and "Ohm out" the test points, to make sure nothing is shorted to ground.
We mostly do very low volume production at my work, so most of our testing is done manually.
We do have a higher volume product, though, that does use a bed-of-nails test fixture. In addition to power and ground nets, we have test points for other functional blocks like Ethernet, SPI, audio (speaker/mic).
If you are doing a first run prototype, you might want to have all those test points for debugging. But in later revisions, after functional blocks have been proved OK, you can remove them from the board if you want.
In the end, it really comes down to your production volume and how much risk you want to take with testing/not testing certain aspects of the board.
This looks like a spark gap.
(You could also look up gas discharge tube (GDT), which is similar to spark gap.)
The likely purpose of this component in your circuit is to protect the rest of the circuit from lightning strike and/or ESD. Spark gaps are often the first line of defense against high voltage.
Advantages of spark gaps: Once the arc is established, a spark gap acts as a crowbar, and it can dissipate a lot of energy. Because of that, spark gaps are used for protection against high voltage high energy threats (lightning, defibrillator). The parasitic capacitance of a spark gap is low, so it doesn't affect the signal. A spark gap can be formed as a PCB feature for free; it doesn't require an additional component in a BOM.
Weaknesses of spark gaps: They fire at a high voltage, hundreds of volts, and the firing voltage is not well reproducible or predictable. To address this weakness, there's usually another overvoltage protection device (such as TVS) in parallel with a spark gap. This additional device clamps at a lower voltage.
related:
What is this component and what is its use?
https://electronics.stackexchange.com/a/28959/7036
EEVblog #678 - What is a PCB Spark Gap?
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IEC 60617 02-03-07how to combine contacts. A jumper has 2 contacts, just bridge these. A test point in form of a pin can be visualized byIEC 60617 03-03-03