1.Have FSG taken LSD and gone loopy or have they actually done something interesting and potentially forward thinking by looking backwards to a man who's his own man?
I do not think Rodgers is a throwback at all, I believe him to be well versed in all modern aspects of the game including the dark arts of stats manipulation. Whatever was said in the press conference about Directors of Football, total control, etc. is a sham. There will still be a structure in place that FSG want, the only difference will be in the titles attached to these roles as "Director of Football" has negative associations in this country.
The success of John Henry and FSG is built on one thing alone - being different. By not facing up to the "big boys" at their own game Henry was able to play the financial markets, by adopting Moneyball he then went on to do the same in baseball. There is no way that the men who only ever seem half interested in football have been charmed by sitting at home and watching Swansea and the press conferences of Brendan Rodgers. What they have been taken in by is a manager who has Moneyball sitting on his desk:

FSG don't care how he looks, walks, talks, or plays football - at the moment that's a happy coincidence. They do care that he speaks their language of stats and, like Martinez, gets more points than his budget says he should. Despite what you read he'll also be open to their management structure, if tweaked a small amount.
Looking backwards? No way.
2. Do you think they will give him 3 years or expect him to get 4th place in a season or was that just bollocks from the people getting rid of Dalglish?
Rodgers will be given longer than Kenny because he is "their" man. They approached him, interviewed him. He fits their structure, their way of thinking and he plays their game. Kenny was placed in the manager's seat by the fans and his excellent first 6 months in charge. "Finish 4th or else" was an ultimatum to Kenny from a group of men unconvinced by the old ways of doing things.
Any failures Rodger's makes will be brushed aside with "long-term" the go-to phrase, a luxury Kenny was never afforded.
3.What are you looking forward to, and what are you concerned about with BR?
A passing side.
A side that bores into the opposition with unrelenting possession.
Taffy-Taka (I made that up, no you can't have it).
As much as I love Kenny we became so old fashioned under him it was embarassing. 4-4-2 every match, Carroll a million miles from the action, Downing on the left and never moving from there, no right winger, 2 men in central midfield not suited to be there (Spearing, Gerrard, Adam).
I want a high-back line, 2 pressing full backs, a midfield 3 that can finally get the best out of Adam and Henderson (and maybe Gerrard), I want Suarez on the right of a front 3, I want passing throughout the entire team, I want Carroll in and around the box like Mario Gomez, I want a high back line, I want a sweeper keeper. I want slow build up or fast counter attacking when it's right, I want bodies in the box even if it risks a counter attack. I want us to be fucking Liverpool and what excites me is I believe Rodgers is the only man in the Premier League who will play like this.
What worries me about Rodgers is his 1 season of mediocrity at Swansea is the greatest thing he has achieved. Leaving Watford and Reading doesn't look good on the CV and he has the look of a man ready to go mental at the first sign of pressure.
4. Is it a gamble or a shrewd investment.... Show us your crystal balls now and in years to come, we'll look back as say "Ah, they knew what they were on about" or, more likely "See, none of us ever know.."
I want him to succeed but it is out of his own hands and entirely in those with the money.
He inherits a side that has a future: Lucas, Henderson, Coates, Shelvey, Kelly and Sterling will all be good enough for Liverpool yet there are still cracks to be filled: Bellamy, Kuyt, Gerrard, Maxi are all past their best and need replacing while there are some areas that are threadbare already (left-back, right-wing) and some that have just poor (Downing).
What Rodgers has been brought in to do is make a little money go a long way. A moneyball man. It has worked at Newcastle this season but if it is a success then, like baseball, every team will try and copy it.
If Financial Fair Play is real, and I don't think it is, then Rodgers should do well over time (which he will be given by the fans for attempting to play football). If it is not then I fear without a new/redeveloped stadium we will be in a perpetual battle for 4th, as Spurs are now, getting it one year and missing the next and being defined by moves in the transfer market.
I do like the strategy FSG want to put in place: use the academy more, buy good for cheap, sell when the price is higher than the value. I hope they have the balls to go through with it because if we carry on as we are, thinking we're in the same league as City, Barcelona, Madrid then we'll be forever doomed.
Prediction: 3-4 season's of fighting for 4th