Designing a bluetooth audio unit for speaker
Is there a way to experimentally find out the power requirement of a speaker?


That's less of a required than a maximum values. Go higher than that, and you damage the speaker; that's an easy experiment, but not very useful to you, unless you have spare speakers...


  The rated impedance is 3 Ω … can support 4 Ω and 8 Ω speakers


Well, that's what ratings are for: to tell you what they promise will work. So, no, from that product page alone, this won't work.

It might be helpful to actually google for the PAM8430and find the original data sheet of the amplifier IC: It also doesn't specify operability at 3Ω. What it does say, however, is that the thing won't output more than 3W. Pretty certain a speaker your speaker's size can withstand that.

Also, a home theater speaker won't be very loud when driven with &lt;= 3W. So, really not the amplifier you're looking for. This thing is designed to drive built-in laptop speakers and phone speakers. (datasheet, first page!)

It also specifies things for 10% THD and 1% THD only: This is not a Hifi component. So,


  Or is there a way I can increase the impedance of this speaker by adding some resistors etc or do I have to search for an amplifier that supports 3-ohm speakers?


I'd recommend looking into better amplifiers, anyway, since you seem to be concerned with sound quality.


  This speaker has +ve and =ve pins, can I directly connect these to the different parts of a 35mm TRS headphone jack or is some other kind of interfacing required?


Not quite sure what you mean here. TRS headphone jacks are not a sensible way to attach a large speaker to an amplifier: they are not designed for the high currents speakers can work with.