What is the maximum size of the MMS message in Android phone? and is there a way to increase this size?
The maximum size for MMS is rather carrier-dependent, and usually is set to 300kB. For your second question, you might want to check Manually edit your max MMS size limit. Another interesting source might be What is the maximum MMS file size that I can send from my MMS phone?
As for changing the limit, there are several consideration to be taken. Sure one can alter any limits, but usually there's a good reason for their presence. As Zuul pointed out (see comment below), you may then be able to successfully send a message of, say, 1MB size -- but that doesn't necessarily mean the recipient is able to receive (let alone read) it. Consider the 300kB limit as "smallest common denominator" between your phones capability, your carriers capability/configuration and the receivers capability.
So if you are pretty sure what you are doing (say, you know your phone can handle 500k at least, the recipients phone can do so as well, and both your carriers support it), increasing the limit might enable you to exchange MMS up to 500k with that recipient -- while failing to do so with others.
To me, this was never a question. If I need send some message, I use email. It's cheaper than MMS, and works between phones and PCs and Macs and... Exception: the recipient has an "older phone model" without email capabilities. But then chances are good it cannot handle MMS either -- so I have to stick to 160 chars with SMS telling him to lookup his mail :)
Basically the size of an MMS message depends on:
There's no definitive answer to this subject due to the dependencies mentioned above. You can contact your operator and try to get a more accurate answer from them. Alternatively you can always test ;)