You should be able to switch in the last 4-6 weeks without penalty (check your T&C's but I have never hit a standard tariff in years). It takes 2-4 weeks.
Don't switch with Uswitch, they are fine to get an idea of prices but there are usually Quidco cashback or referral codes which get you some money back (often £50+). If you use uswitch then they get the cash and they don't actually do anything except pass your details to the supplier, there is essentially no difference when you engage the supplier yourself.
The rules mean you don't need to notify your current supplier, you just engage a new one and the two suppliers deal with it between them. You just need to take a meter reading when your new supplier tells you to.
There shouldn't be any link between your homecare and your energy supply, the former is essentially an insurance product but you may get a discount if you have both off the homecare but it shouldn't stop entirely, anyone can get it BG customer or not. You will need to check that with homecare but I doubt one will effect the other greatly.
Energy tariffs are very regulated and they can only have a few and all charges must be clear and upfront, there should be nothing hidden. Always base your caparison on your actual usage over the last year. Most on here (me included) advocate for setting up a quick excel to compare rather than relying on a comparison site as there are extras that are often not taken into account like Quidco and if using a comparison site make sure you tick the box that says 'show me the whole market' on a comparison site and not just the ones they can refer you to.
I guess as the 2 companies talk to eachother there will be no loss of service or getting cut off etc 
