Tvheadend

Can 1 tuner do multiple channels on 1 transponder?

Yes - while I've never personally deliberately tested it, I've read elsewhere that channels on the same mux should be decoded by the software in parallel. I'm sure I've recorded multiple BBC HD streams on a single tuner, though.

Can the stream output in UDP so it can be picked up in another platform (non Android)?

There's nothing Android-specific about tvheadend - it can pass the stream to tvhguide (the Android client you're probably thinking of), XBMC (on any platform you can imagine), and VLC (ditto). All you need to do is lock onto the right stream... I believe that this is HTSP, so TCP instead of UDP, however. I think you can use VLC as a proxy to re-broadcast as UDP if you really need to.

What are the recommended requirements for running 4x4 tuners outputting 16 channels?

Depends on your system. USB tuners tend to meander between different device numbers on a reboot unless you take steps to lock them down, so internal tuners are probably preferred - although I use PC-TV external tuners and they work well.

TBS does some good tuners, but the drivers don't play nicely with many non-TBS devices - there are many discussions. Indeed, there's a whole thread here dedicated to "what hardware...", so that'd be a good place to dig.

Thank you.
I am interested to learn how to stream 2 channels from same TP with only 1 tuner. Do I just add the required mux and links for available services should work in parallel?

Yup, exactly that - two requests from the same mux at the same time should work fine. You'd need to test to be certain, though, unless someone can stumble in and confirm...

I will spend some time today or tomorrow and check whether I am successful at this. If so, will post back with instructions. If not, will post back with logs

One more question, to preserve bandwidth(since this TP is all MPEG2) what would be the best option to trancode the video to H.264/MPEG4 this(preserving the cost as well)
Few options I've looked up:

Wowza
VLC
Third party transcoding(have no been able to find any feedbacks)

Thank you.

tvheadend has native transcoding - search around here and you'll find some information. Of course, that does rely on your hardware being up to it, especially if you're up to HD streams as transcoding two simultaneous 1080 streams to H.264 in realtime is no small demand...

If it's not realtime you need (e.g. you just want to squash down recordings) then you can use ffmpeg or Handbrake in a post-processing script.