Q: Can I use barrel connectors to lengthen cables?
A: Yes you can. However, it is not recommended. Barrels in the line can cause signal loss to the receiver and voltage drop to the LNB. If you choose to use barrels make sure that they can pass 2150 MHz and 19VDC. Also make sure that you use RG-6 cable with the same specs as above. It is also recommended that you do not bypass the system ground. If the install was completed to standards; the tech would have ran coax to a ground block, bonded that ground block to the home's electrical and then ran another line inside to the receiver.
Q: Also, I discovered the installer used one of the two cables from dish to split to inputs on the 722. Then he connected the second cable from dish to the ANT input. I realized he wasn't the sharpest when he was on site, but hard to believe. Is there any advantage to eliminating the splitter and just using the two cables to the two SAT inputs?
A: I am assuming that you are using the 722 as a two room setup. If this is true then the installer ran one line to the in/out of a diplexer. One side of the diplexer went into the separator and the other into the home distribution port on the receiver.
If you do not already have the tools (compression tool, cable stripper, compression fittings, etc...) you may wish to consider having a pro rerun the line. You may also be able to have Dish come out and move the lines for you. If you have the service plan they should only charge you $15. Just tell them that you want to move your equipment/lines and it should not be a problem.