If I choose to play online do I keep my Sidey and the upgrades I've made or start from scratch?
Yes, you keep them. You can switch between all modes and everything you have done, achieved, purchased, made friends/enemies with etc remains as is. You can switch to Solo from Open right in the middle of a mission, if you like.
I was expecting to get blown up for smuggling illegal goods but you pay a small fine only?
I think it depends on the cargo.
Being scanned with cargo marked 'stolen' might get you in trouble, but I believe you can now hand it in and get a reward, so not sure on how that works these days.
Used to be stolen good would get you fine, while outright illegal goods would get you Wanted and a small bounty on your head... Again, you used to be able to pay this off at most stations, but now they last a certain period of time, during which you're well-advised to stay out of that system or deal with bounty hunters and cops.
Guys, there is any popular starting point/system for peacful starters?
There are less populated systems (see Galaxy Map and sort on population), although if it's mainly players then anywhere away from the starting systems and surrounding areas will do. So long as you maintain your neutrality with local factions, most NPCs will leave you alone, too. Just the ocasional pirate to watch out for.
I've not messed around with this power play stuff yet, how much actual difference can a player, or group make?
Theoretically, a lot.
But bear in mind that while you may have 50 people all rooting for Felicia Winters (who is kinda hot in a Powersuit Dykey sort of way), there may be 100 horny schoolboys supporting Aisling Duval and 2000 of us lusting after the more MILFy Arissa Lavigny-Duval...
The biggest individual impact you'll see is the weekly 50 Million Credit payments, once you reach 10,000 Merit points (or lower payments for less points). You'll find systems increasing production on goods, which means you can buy cheaper and sell higher elsewhere. You'll find more friendly ships nearby to come help you out. You may also start finding Outfitting has some interesting new items.
I'm looking forward to trying it out, but won't be pledging to anyone until I have my new ship.