1) Do I check in the macbook together with my luggage or carry it onboard?
Electronics and batteries should never be put in checked luggage. They are too fragile and also vulnerable to theft.
2) I have a separate laptop bag for my macbook and I do not want to squash it together with the backpack I wish to carry on board..so can I have two carry ons - my backpack for clothes and the laptop bag with my mac?
An ordinary backpack and laptop bag should be fine. You can check the size limits for carryon luggage for your airline on their website. If you also carry a purse, even a small one, you will probably need to squash it into one of the other bags, so that there are only two "items". LHR is known to be picky about this.
Is there a 3?
4) I am going from Changi to LHR and onwards...will I be asked to switch on the macbook or take it out and show them any such things by customs for them to check or whatever they do?
At the security check, you will have to take your macbook out of its bag; it goes through the x-ray machine separately, but no differently than any of your other belonging (i.e. in a plastic bin, not directly on the belt). It's extremely unlikely that you would be asked to turn it on. As long as your macbook is for your personal use, customs is not involved and there is nothing to declare.
5) Do I put it through the x-ray machine, will it damage my apple and make it a lemon? I will also be bringing along an external HDD, will they x-ray it too?
The x-ray machine will not damage your macbook or HDD drive in any way. You should probably take the HDD out of your laptop bag, along with your macbook. It is
extremely important to keep a careful eye on your belongings at the security check: with your things spread here and you there, it is a big opportunity for theft.
In any case, it is always a good idea to keep your computer data properly backed up.
6) I arrive at LHR Terminal 3 and then have to catch the next leg of my flight at Terminal 5..are the two terminals far away? Will I have ample time? How do I get from T3 to T5? I have a 2 hr layover at LHR.
Follow the 'flight connections' signs to terminal 5. You will probably be able to get the boarding pass for your connecting flight at Changi; if not, you will get it at the transfer desk. Carry a paper printout of your itinerary, to show your connecting flight. You can also look at the LHR website for more information
You will pass an extra security check in LHR; this may involve a revealing scan of your body, as well as your things. Try to avoid this, if possible, as radiation exposure is not healthy. If you are selected for this, it is not possible to avoid. If you are wearing a sanitary napkin or similar, you may be questioned about it. You will not need to go to passport control and immigration, since you are not entering the UK.
Two hours is sufficient, but not generous, for an LHR connection. If you are traveling on a single ticket, the connection will meet the airline's minimum connection time requirements and they will be responsible for forwarding you if the incoming flight is badly delayed.
Needless to say, I m sooo looking fwd to travelling on the A380 to LHR. It will be in economy but still its sweeeeet.
Have a nice trip.