I added another comment elsewhere about having the bike since about '87 second hand, but with only 750 miles on it. I haven't been able to ride since I became somewhat disabled in 2004. I still have the Maxim.
I regularly got about 45 mpg, did a lot of fast riding, and always enjoyed gunning it when getting the green at the traffic signal. I have made no engine modifications. If you're getting 20mpg, something is quite wrong.
As far as the cold starts, I had a similar problem the first year on cold mornings in upstate New York. I remember running down the battery trying to get her to get up and go. I may be over simplifying the issue, but refer to the chart in your owners manual and rule out the problem being the grade of oil you're using. She seems a bit more sensitive to low temperatures than indicated. It made a world of difference.
If it is hard starting, then it could be several items.
Number one is check the water level in the battery by removing it and giving it a flat slap on the side. Then put it on a flat surface and rock it back and forth several times. That will knock the air bubbles to the top, and drop the battery fluid level to a realistic reading. Refill with only steam distilled water, and if you have a charger, do an overnight charge on it.
Next, check the plugs for proper gap, and while doing that, look at the plugs for coloration. If the coating is not a light off white color, then it is running too rich, plus make sure all four cylinders have plugs that look exactly the same, otherwise you can have a clogged carb jet.
Another trouble is age cracks in the insulation of the coil pack. You can wrap it in electrical in multiple loops to seal it, or do like I did and get a new one. With it set up right, I get well over 40 MPG at the worst in city driving.
With a good battery and plugs, plus a good sealed coil, mine starts every winter day, and for the first 17 years I had it, it was always parked out doors in New England weather.
If your speedometer stops from time to time, or other instruments die out (mine often stopped displaying the temperature), check the instrument ground wire. It is in the middle under the gas tank. The bolt holds the thermostat and water lines in position, and can't fall out, but it can come loose. Just tighten it up and all the instruments will work right. Only other reason for it to work intermittent is the speedometer cable has a locking tang on it that is clipped into position on your front wheel. If it is broken or your locking bolts are loose, it will slide. In either case, if your ground wire is not loose, then you need to check it out right away.
As for the leaking fuel petcock, there was a warranty recall years ago for that. Replace it before you have a fire while doing 60 MPH.
I've owned this bike for about 7 years. Sold it and regret it. For the money, this was the best bike I ever had. I'm looking at one right now. MPG should be about 34 to 46 MPG. 34 when you're gassing it and 46 highway cruise. I checked often and assume this is rather accurate. Maybe with abusive riding 30 mpg, I don't see it though. Those are the numbers on my bike, checked on a regular basis.