If your computer can play a regular DVD, then it should have the right codec to play .ts files too.
K-Lite Codec Pack will have the DVD codecs required if not.
Not necessarily. .ts (Transport Stream) is just the container that contains the video, audio and subtitle streams (if subtitles aren't hardsubbed or absent).
I'd recommend trying
Media Player Classic - Home Cinema. It has support for a bunch of different codecs as well as hardware acceleration support for H.264 and VC-1 (the most common codecs used for HD material). If the files can be played with MPC-HC, press
File and then
Properties. The tabs
Details and
MediaInfo should offer more information as to which codecs have been used to encode the video and audio streams.
As for converting to .avi or .mpg, there are two ways to accomplish this.
1. Multiplexing.
Basically just copying the audio, video and subtitle streams into a .avi or .mpg container. No loss in quality at all. This does however require the audio, video and subtitle streams to be supported by the container. And if the streams are big, then .avi or .mpg containers may not support the size and would have to be split into several smaller .avi or .mpg files. The Matroska container .mkv is the most flexible container currently out there.
AVIDemux can be used to multiplex the .ts into a .avi file if the stream formats are supported by the software.
2. Encoding.
Encoding the streams and using .avi or .mpg as the container. Loss of quality (how much depends on the used codecs and settings) but easier to get container compatible streams. You can also deinterlace the video material when encoding the video stream giving you better video quality than if you were to use a media players deinterlacing filters. Technically speaking this method also contains multiplexing.
AVIDemux can be used here as well.
Handbrake is another great tool, but has dropped support for the .avi container (
0.9.3 does still have support for that).
My suggestion would be to multiplex the streams from the .ts file into a .mkv file with
MKVToolnix. However the .mkv files aren't supported by DVD players and most stand alone players (except for Blu-ray players and some devices like Western Digitals TV Live, but even then the streams have to be encoded with the right codecs). But that shouldn't be a problem since you want to watch them on your computer. And if you want to watch the videos on other devices, then you can use the .mkv files as the source material and just encode the files needed from those.
EDIT:
A friend scanned the video with MediaInfo: my ts file isn't a normal ts video, but is a cripted ts video. How can I decrypt it? I used DVD decrypter but it say "unknown file format"
Unfortunately, I don't think the forum rules allow for discussion on how to circumvent that encryption. And it may be impossible (in a practical sense) to decrypt depending on implementation.