Hello DFRPG Board

I'm currently GMing a Dresden Files game and i really have some problems.

1. I'm constantly having problems with the investigation part of my games. Having the whole city to go looking for information seems to be to big for my players and they constantly lack ideas for finding clues.
The wizard in the party sometimes figures out ways to use his thaumaturgy to find clues but the ninja-detective-werecat character has problems using her skills to her advantage.
Another problem for me is that i'm bad at helping them figuring it out. How should i give them clues without going "yeah you just need to go to this place over there and you will find everything" - that would be boring.
I have no idea how they will try to find info so it's hard for me to plan that or to even know how they could get that info.
I have run good "hey, that's the problem" sessions and good action ones, it's that legwork and detective thing that troubles me.

2. I'm lazy. I'm constantly underprepared and have to run a lot of stuff on improv. That's okay for me but the game is lacking because of that. Any tips for GMs that don't like to plan that much ?

3. My PCs right now have a job from the Summer Barons of the city to find out why some Summer Elfs attacked a group of anti-mining demonstrants.
At the same time they had to find a group of missing persons. Clues lad them to a museum where they found a sorcerer, enthraling people. After chasing him through the museum and the streats they battled a troll he had called for help. The next day the wizard conjured a water spirit to find him. The spirit warned them that this guy is the Black Miller (a fairy tale figure from our region), a sorcerer in pact with the winter court of the sidhe. (Our city is in summers territory, they try to get in)
The next session will be about them storming his home and finding proof that he tricked the elfs.
He has his home in a puppet theatre (because it's scary)
I want to try something a bit different, the session will start with them, captured and bound to chairs while the miller laughs at them. Then cut to the morning before. Should i do that or is this to railroady because they could try any kind of security measure possible and will still be captured...
Anyway, i don't want them to capture or kill him because i want to use this guy in following sessions and he, as a caster, can be quite deadly to them.
What can i offer my PCs to give them a satisfying ending to this story arc ? He could maybe collapse the house arround them. They will have to get out of their binding and then have to find a way out. (but that isn't enough i think)
Please playground, do you have any idea what i could do ?

4. problem : We only have time to play 2-3 hours every week and i have problems using that time effectively. Sometimes we spend this time and not much happens in the story because they venture of in a "wrong" direction or just RP without much story happening. What can i do to make the most out of the limited gametime ?