How do I read these (Arduino) schematics?
This is a horrific schematic and I can't blame you for being confused.  


  "Are there connections omitted?"  


Yes, one would wonder if they forgot to connect them. They do have a net name next to them, however, and you'll find that same net name back elsewhere on the schematic. Everything with the same net name is connected. Personally I prefer the use of ports to indicate this, so at least it's clear it's not a forgotten connection.  



I commented on the following part of the schematic in another answer:



Here there's too much unnecessary information shown, and required information is missing. It's probably not clear on first sight but that "TS42031-160R-TR-7260" refers to the switch at the top, just like the word "RESET". That's the reset switch, but it would be much clearer if it only showed the refdes (that's short for reference designator). Each component has a unique refdes which identifies it. For a switch it could be SW1. The long type number is completely irrelevant to understand the schematic and it shouldn't be here. Your schematic should only show basic information, like "R22" as the refdes for a resistor together with its value, like "12k". That should do. Whether it's a 1/4W or 1W is not important to read the schematic, so leave it out. This kind of information, just like the manufacturer's ordering code belong on the BOM (Bill of Materials) which you want to have next to your schematic in case you need the extra information. The question about the power of the resistor may come up in a design review: check the BOM.

  

This may be the worst part of the schematic, and you'll only understand it with a lot of experience and some guessing. It doesn't say anywhere, but these are the power connections for the dual opamp U5. It seems to be the only IC for which no power connections are shown, and a dual opamp in an 8-pin package often has its power on pins 4 and 8. (That's where experience comes in).

All in all, this is not a good example to learn reading schematics.