Could I use a DSR-11 with an FX1
 

In DV mode to record the longer length tapes to get a 2 hour recording? I'm assuming it can't be used in HDV. Or is there a better deck that does both for this cam?

You can't record in DV mode on DSR11, just DVCAM. You can use big DVCAM tapes to get 2 hrs or more.

You can record in DV mode, but only in SP. So, it is up to you to
decide if you want to use 83 minute small tapes to master to in DV
or the big DVCAM tapes which will record over 3hrs on the 184mins.

And no, the DSR11 WILL NOT playback HDV tapes. If you are doing
only HDV, I suggest looking to get a Sony HC1 to use as a deck.

You can record direct to a laptop, either to an internal or external hard drive, limited only by the size of the hard drive (or battery power, if not powering the cam and/or laptop via AC adapter).