camera-dept MTS to MP4 converter and portable camcorder monitor questions

Hi, I have a Canon Vixia HF200 just learning how to use and 2 basic questions to start with. One is can anyone suggest a good free downloadable MTS to MP4 converter program for Windows 10? I've seen Freemake and a Windows editor and some others that all say free trial, but haven't seen anything that says how much it will cost after the free trial is over. I'd like to eventually do some simple editing also and feel there must be some fairly easy to use and free or reasonably priced basic editing software available but don't know how to figure out what would be good to get since of course they all claim to be. This is all just for personal use.

Another question is about a portable monitor. The camera has a mini HDMI out and using a mini HDMI to regular HDMI cable can use my TV as a monitor. But is there a small tablet size monitor that is easy to carry around and will run on battery power or an external power input? And reasonably priced? I see some on ebay for around $80 and they have a DC input but don't know if they will run on a battery or not.

Thank you for any suggestions!
Maine, USA
If you are wanting your videos in a different format so your video editing program will recognize it, conversion is unnecessary and will likely introduce quality loss unless you use something really involved and space-consuming such as avisynth. You only need to re-wrap your file(s). It is 100% lossless. Shutter encoder will do this (and many, many other things) and it is free. The download will mention a donation, but you don't have to donate. If your download has a problem starting on the download page, click "Where is my download?" and choose it from there.

From the Shutter encoder main menu, load a file by browsing or dragging it into the window. Under "Choose function", click "rewrap". To the right of "rewrap" where it says "none", click to open the drop-down list and choose your desired video container. Choose a destination folder or leave it default. Click start function. Your video will be done very quickly, usually in seconds. You can also choose to re-wrap only specific segments of a video with no quality loss. There are also numerous color correction and enhancement options.

Your can use an android device as a monitor if you have one.