Identify an inductor on a PCB
The first inductor has red lines, not brown, so it is a 2.2µH valued inductor with 10% tolerance.  10% tolerance components can't be valued with 1.1 - it's just the high half of a 1's tolerance, or the low half of a 1.2's tolerance. You can have a 10% tolerance 2.2 valued component though. See E Series.

Anyway, inductors not magical or unicorns, you just buy them like any other component.  You don't wrap artisan capacitors from scratch or make oven baked carbon resistors, right? Well...ok, that could be fun.  But winding inductors can be two things: terrible, or really terrible.  

Inductors, inductors everywhere!

I think the 16¢ is my favorite.  Entirely because it's 16¢. The 'saturation' current is the maximum current you can put through it.  Size to your needs.  More turns around a core increases inductance (in fact, inductance is proportional to the square of the turns) but at the same time decreasing the saturation current.  For this reason, inductors of a fixed size will see a drop in saturation currents as their inductance values go up, and vise versa.  2.2uH is nothing, so even tiny cores happily exceed the current rating of the wire around the core.  There is not a 'wrong' choice amongst the entire list of inductors I linked (I think).
The second inductor is a capacitor.  It's a Murata TZ03 trimmer capacitor.  They don't say what their value is, but its probably a dozen picofarads or so.  It is used to tune the remote to the right frequency.  There are a very small number of possible trimming ranges, you'll either need to buy a meter that can measure capacitance with picofarad resolution...or trial and error.  Try a 4-60pf trimmer or thereabouts, the value is almost certainly going to be somewhere in that range.  If its not, Murata only makes them up to 220pF. Not to many possibilities.

Good luck! 

Update: Thanks to Respawned Fluff and his very helpful comment, I think it's same to assume the trimmer capacitor has a range of 2pF to 6pF. I didn't realize the TZ03 type trimmers are handily color coded based on their value.  Looking at the data sheet, blue means it's range is 2pF to 6pF.  This is the same across their entire TZ0X line it looks like, so it's probably a pretty safe bet. 

Murata's Datasheet