Poor FM Reception

I can't tell you how good an outdoor antenna is compared to ANY little inside antenna with an amplifier.  Absolutely amazing.  If you can install one with a rotating mast that's even better.

Two things to consider:  The antenna cable must go through a grounding block which is bonded to the same ground as your home before entering your home's perimeter.  Not another ground rod, or water pipe.  Second, because you run the risk of lightning entering your home I strongly recommend the use of a coaxial surge protector ON the grounding block, like this gas discharge unit. 

Because of this, it's a good idea to check where you have access to a house ground before committing. 

OTOH, a half way decent middle ground is an attic mounted directional antenna, which doesn't need the grounding/surge protection. 

Agreed that the outdoor antenna is the answer to you problems.

You will want to try the outdoor antenna with and without the amplifier. If you are that close to the transmitter, the amp may overload (not causing damage), the front end of the tuner. I've seen incidences where a station splatters over to adjacent frequencies because of it.

Solar panels will generate radio frequency interference (RFI) when the invert  DC voltage to AC.  This will disrupt broadcast radio frequencies.   The panels themselves represent an additional layer of material to block or reduce indoor antenna radio frequency reception.  Potential solutions:

1. As you indicate, go with an outdoor antenna.  Install the antenna above the highest point of the panels on the roof.  Locate the antenna as far as possible away from the inverter.  
2. Assure solar panel wiring is shielded.   On simple and inexpensive solution is to place ferrites on the wiring between panels, and the leads in and out of the inverter.  

I am a Ham Radio operator. There is no interference from the solar panels and It would show up much greater on the lower Ham radio frequencies,

I live in a remote area where there's few stations and the only operate on 5,000W daytime and 500W at night. Those expensive Term antenna's are no good but I found an amplified rabbit ear after trying 4 other antenna's for my vintage McIntosh MR-71 tuner that works great. Home Depot online. $18 free shipping. It is a NAXA