Do I need to register or declare the computer I will be bringing from home for Britain travel? I heard there may be a problem on leaving England?
Not sure what problems you might have. I have travelled at least 4 times with mine and never had a problem. You are going in as a tourist (I assume)so that should not be a problem, you do not hav eot declare it. Coming back to the US you may have to prove you did not buy it when you were away, but ythat should not be difficult, at worst you can show files that you created prior to your departure date.
As for airport security, I have found it straightforward. Normally you have to take it out and sow it separately. This happened whether it was in England or anywhere else. In Venice they took mine and did a swab of it - I do not know what for unless they were testing for explosives, but it only took a minute.
I doubt if you will have any problems with it.
My husband and I just came back a week and a half ago from Munich and London. We didn't have problems in either place. You just have to take it out of it's case and put it through the machine by itself just as you do here in the States. We were never asked about it and didn't have fill any forms out either.