If the car is only driven about once a week, I suspect condensation in the fuel is a likely problem. Add a couple of bottles of dry gas BEFORE refilling the tank, then add one more per fillup for the next few tanks.

Especially in fall and spring, the large swings in temperature invite condensation problems. The less full your tank is, the more moisture-laden air over the gas is available to creat the problem. For cars driven infrequently, keep the tank 3/4 full or more. The last two gallons costs as much to put in as the first two gallons.
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Thank goodness we don't get all the government we pay for. -- Will Rogers

Doesn't necessarily line up with your symptoms (other than the hard start), but you should check your crank position sensor (CPS). Sits at the back of the engine, atop the transmission bellhousing. Cord comes up to a plug near the large, grey plug at the back of the engine. If this hasn't been replaced, it's overdue. The shielding on the wire starts to break down and will cause the sensor to tell the ECU that the engine isn't running or trying to start and cut the fuel flow. ~$25 and a simple fix, if in an out of the way location. Search the forum for a full writeup with pictures.

Good luck,
Zach