the p0131 is for an oxygen sensor low voltage, which would not be causing your limp mode issue.
The p0705 however, Is what is causing your limp mode issue. I have seen this exact issue before a few times and want to you to check the connector above the trans pan on the transmission, ill attach some pictures.
What happens is fluid can leak from that seal, and then inside the connector, and get into the contacts of that connector and cause a "short" or what the computer sees as a short.
One you seperate the two connectors, you will need to use a 7mm socket to get the old connector out and go to the dealer to buy a new one (Which comes with new seals) then just push it in, install the 7mm screw, spray off the other end of the connector with electrical parts cleaner (Can be had at any auto parts store) reset the light, and thats all there is.
It may seem a little intimidating to tackle on your own, but take a look under the car after you see the pictures I am sending and its not to difficult.
please feel free to ask me any other questions you have after reading my reply, I would be more than happy to answer them.
Also, please do not forget to rate my service since that is the only way I get credit for my answer from this website.